Loud Flower prints all our fabric goods exclusively with water-based inks, and yes, they are totally washing machine safe and durable!
In the world of screen printing, there are two main types of ink used. The vast majority of commercial printers use plastisol inks (aka plastic-based). These inks definitely have their advantages: infinite open press time, complete coverage, and lower curing temperatures to name a few. BUT they are also made of plastic and harsh chemicals. This means that 500 years from now, when the cotton of your shirt has long decomposed, the plastic particles that made up the graphic will still be on the planet.
Water-based inks will decompose right alongside the cotton. They also have an almost invisible feel after their first wash for the softest wear around. For me, this makes water-based ink's slightly more difficult and limited printing processes worth it.