Q:

Which martial arts styles work best with social distancing? 

Yesterday, I saw a woman and a young boy sporting their TKD gear, shopping after class.  I wondered what their school was doing to meet social distancing guidelines. 
Wear a mask?  Probably, not. 
Stand six feet apart.  Wash your hands.  Don't touch people or your own face. 
With Covid-19 cases increasing, I don't feel comfortable going to a gym or martial arts class yet. 
UPDATE on July 4th, Independence Day: The answers provided to this question helped with my internal dissonance regarding returning to martial arts training.  I will wait. 
On Facebook, I found photos from two well-known, local jiu jitsu schools showing students and teachers training pre-Covid style. 
The photos were posted in June, some a week before masks became mandatory in my city.  I understand the need to avoid bankruptcy.  I even understand the disagreement about wearing masks and social distancing.  But how are they getting away with this? 

Beaches are closed in some areas.  Restaurants and bars are heavily restricted and carefully monitored.  Some have gone out of business because they can't operate effectively. 
I feel sick to my stomach looking at these images.  I know how much fun training is.  Yet, if the health advisors are right, then training jiu jitsu -- without a mask is wrong. 
The dissonance is back.  Reckless disregard makes it hard for me to trust the leaders of these schools.  I'm pulling my weight, wearing a mask for the last three months, to help fight Covid.  And yes, my disagreement is my business.  Their lives.  Their risk. 

A:

In the era of COVID-19, partner training is a bad idea.  You do not want to spend extended periods of time breathing heavily in the same space, and especially not indoors.  Grappling is particularly risky. 
Many martial arts already include social-distancing-ready methods in their standard training that can fill your social-distancing training hours.  Many of these methods are not suitable for partner training, so now is the ideal time to get full use of them.  They do not substitute for the fighting skills you acquire sparring and partner training, but those are not available right now. 
I will avoid evaluating styles and instead point out elements that can/should be practiced with social distancing.  Lots of styles have these elements, so I will point out a few examples and leave evaluation to you. 
Forms
Forms training is the foundation of many martial arts body development.  Forms usually combine elements of speed, balance, leg strength and flexibility, coordination, mental focus, and prototypes of martial techniques together in one package.  Styles using forms include kung fu (in all its flavors), karate, and tae kwon do. 
Depending on your social distancing risk tolerance, you may be comfortable having a masked instructor stop you periodically and make physically adjust your body.  The time they need to be near you is short and they can otherwise be at a distance.  Otherwise, the instructor can demonstrate at a distance and provide feedback.  Outdoor forms practice would be preferable to indoor. 
The general problem with forms is that styles can have them without being able to fight.  But you should be able to imagine that someone able to fight can give you sequences of movements to work on, and those sequences can be called forms. 
Basics - Footwork as an example
Most people are not willing to invest the time in learning "basics" that they could because sparring and other exercises are more fun.  Now is the perfect time to focus basics you can practice alone because your partners are not available.  This analysis is based on my study of bagua, but I expect you will find it applies to boxing, kickboxing, MMA, etc. 
Let's assume your style has a fighting stance that you use.  Enter your fighting stance, then take a step forward. 

Are you immediately in your fighting stance again?  Or is your spacing off? 
Are you immediately balanced, or do you need a moment to regain your balance? 
Are you on balance as you move?  If someone were to grab your belt (something around your waist) and then you step, would you be leaning to move forward? 
Do your legs drive your movement when you step?  Or do you fall into your step? 
Is your step fast, or is this a great time for a sparring partner to sweep your feet? 
Now that you have tried to fix several different things, are the earlier ones still fixed? 

OK, so now that you have fixed all of these things, you can add steps in other directions.  You probably at least want to also step angled to the left, step angled to the right, and backwards possibly also to the side.  Presumably you started facing an opponent, so as you move to the side angles, you will want to turn towards your opponent. 

Check all of the above items again for each direction
Now that you are turning as you are stepping, are you leaning as if banking into a turn on a bicycle?  Do not lean because this puts you off balance. 

Now you can step in multiple directions. 

Can you react from your fighting stance to move in each direction equally well?  If not, why is this your fighting stance? 
Can you move in any direction at reflex fighting speed, or do you stop to think about it? 
What happens when you practice stepping in a field where the ground is not perfectly flat?  Are you tripping over the little divots animals have dug? 

You can practice all the footwork alone, although it can be helpful to have partners provide moving resistance or other feedback.  It takes a surprisingly long time to learn footwork, and honestly the training can become a slog, but really at some point the footwork becomes advanced and not basic. 
We have not even started on the hands yet, but this is enough. 

A:

The only martial arts training that makes sense if social distancing is a priority is getting strong and fit in your home gym.  Make of your body the strongest, fittest, fastest, most agile, flexible, and powerful version of itself it can be.  When we have coronavirus treatments and vaccines so we can do contact training again, do that. 

A:

Which martial arts styles work best with social distancing? 

I will talk about the striking arts (e.g., boxing, kickboxing, taekwondo, karate, etc.). 
Working with non-humans:
Heavy bags are your best option now (from your YouTube channel, it seems you have some decent experience in striking).  Most gyms where I am have opened with the policy that students will book sessions in advance to come in and work on the bags (heavy bags, speed bags, double-end bags, bobs, and other stationary striking dummies).  This makes sense because each student is given a bucket with some cleaning agents and towels to wipe off the bags before and after use. 
Some gyms have done an excellent job of creating "work pods" — square shaped designated working spaces marked with colored tapes around heavy bags.  There is decent amount of space to work around a bag.  Depending on your gym, you can book your session in splits; for example, a 30-30-30 split, where you work on a specific "working pod" for 30 minutes before moving on to a different one.  Note that there are other students who are also working on the bags.  So, the designated working areas ensure that everyone follows "social distancing" guidelines, and that all students have a safe working environment. 
Working with humans:
This is a little complicated.  In my region, some gyms have started classes (boxing/kickboxing).  Again, the number of students per session/class has been reduced, and each student has their own "work pod" for that class.  The classes mostly include

some high intensity cardio and stretching,
fast paced combo work (which the instructor calls out),
fight breakdown on a projector once a week (this is new, never done before) where the instructor explains techniques and strategies from classic fights,
and finally, some pad work only for advanced level students (consider them regulars, have been coming to the gym for a long time, are matured enough to understand the well-being of others). 

But this is very rare.  In my region, there has been very few COVID19 cases so far, and gyms are strictly following rules and regulations outlined by the local government.  These policies are not recommended for all places. 

Wear a mask?  Probably, not. 

It is irritating to do martial arts wearing a mask at a high pace.  However, I have seen students wearing masks made of very thin and light material in the gym.  I will say this though, with the cloth mask on, you can still shadowbox at 100%, maybe for fewer rounds.  And if you are working with a partner, having the mask on is a good idea. 
If you know and have people you trust to work with, people who take precautions with utmost care, you can do some long distance pad work with foam pool noodles.  But really, this is up to you; you will have to make that decision along with your peers.  Anyways, note that in the video, they are standing quite close to each other, and Shane is  not holding the noodles at the end.  If you hold the noodles at the end, you can increase the distance between you and your partner.  Also, you can use longer noodles. 

For kicking, you can use the taekwondo kick pads.  These should allow you to have some space between you and your partner.