'should' from whose perspective though? 'Sites that don't want Tor users' have no incentive to care do they? If anything it stands to reason such a site would block anything and everything to do with Tor, using it as a search term, usernames containing it, anything?
(I don't know much about Tor, so am I missing something about 'middle relays' that such a site would want to allow them?)
Edit: oh is the point that you're not accessing the site using Tor, just from an IP addociated with Tor use?
Exit nodes are the interface between Tor and the "clearnet" (regular internet), whereas relays just relay traffic between Tor nodes (to make it harder to trace the route). So there wouldn't be any Tor traffic from this person's IP going to websites.
Presumably most folks neither know or care about this distinction and just block all Tor related infrastructure outright, since some of the traffic coming through is malicious.
Frankly, as the OP stated, one reason to use a tor relay for direct traffic is to hide your traffic. A bit like a guy in a trench coat and fedora trying to look inconspicuous.
It's not illegal, but it's also not surprising when such folks are escorted out.
(I don't know much about Tor, so am I missing something about 'middle relays' that such a site would want to allow them?)
Edit: oh is the point that you're not accessing the site using Tor, just from an IP addociated with Tor use?