It's safe to run relays at home but not exits.
Various organisations will deny their services to you just for running a relay, despite the fact that no proxied traffic will exit your network and connect to them. I hope that it is incompetence, it's often unsurprisingly difficult to contact anyone who's able to deal with the issue.
Amazon Video is a high profile example.
You then get people who operate lists of all relays e.g. https://www.dan.me.uk/tornodes
There's probably a good reason for using a "full" list, but I can't think of one off the top of my head. That site at least offers both and just about explains the difference.