Neighbor's online platform is extremely safe. All of your information is stored responsibly and will not be shared, and its secure payment processor will ensure that your transactions go through without a hitch.
In terms of the safety of your actual extra storage space experience, Neighbor seems to do what it can to keep it as safe as possible by vetting people when they sign up.
That said, no matter where you store something, you're always running the risk of something going wrong. Whether you're using someone's garage or a traditional storage unit, 100% security isn't possible.
With this in mind, there are a couple of things to consider. In general, you'll want to steer clear of storing highly valuable or highly sentimental items any place other than your house. Liability protection is great, but it can't replace lost items if something happens.
You'll also want to consider a particular host's rating on the platform. If someone has a less than ideal rating, it’s probably safer to look elsewhere.