In practice I doubt Americans would end up qualifying for refugee status, at least not yet. I'm pretty sure you have to show there are no safe places in your country, and many US states are more reasonable for LGBT folks than some Canadian provinces are.

The UN has expressed concerns about Canada designating the US a safe country and asked our government to stop this. I'd be surprised though, if either major party listens to them about it. :/

The safe third country law predates the bulk of the current insanity, and Canada wants to maintain decorum with Trump due to ongoing tariff and sovereignty threats. Dropping out of that agreement shouldn't be required to accept someone's refugee claim and requires less political capital.