I'd avoid hosting a tor exit node at all costs, considering that they are a lot of bad actors on tor. Even some 3 letter agents can host cp on your tor sites and then accuse you.
Well they can probably put illegal material in your apartment and then accuse you.
this usually last resort with hopes of eliciting self incriminatory statements.
i.e. [i didnt do the CP i was just snooping servers]
You can't use exit nodes to run "tor sites", because they only allow outbound connections. You can run hidden services, but they work entirely through relays (ie. not exit nodes). Given that hidden services are end to end encrypted (none of the relays in the middle can see the traffic), and to my knowledge relay operators have generally not been prosecuted, your specific scenario is unlikely to play out.
That said, if you're running a exit node and the FBI wants to frame you, they can still use your relay to conduct some illegal action (eg. uploading CSAM to some clearnet site), and pin it on you.
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