It depends what you mean by "safe".

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.

I've been running relays at home for over a year. The only sites I have trouble with are Monoprice and Apple Support Forums. I don't have any trouble watching Amazon videos.

How do these various organizations know you are running a relay?

Due to the nature of the tor network, relays aren't a secret. They need to be public so clients can independently choose which to use.

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.