The problem is that "fascist" is being used to label people who are nowhere near the point of racism, Nazism, and falangism.
The RUP and Conservative parties would never have gotten the support they did if they were run by literal Nazis. We're not all MoonMan.
To be fair, BTA is not entirely liberal. OlympianProduct and SurlyKong69 are conservative, and they're in CTL/BTA, but they both have done so primarily out of opposition to BritishMormon, out of the belief that he is the deleted IncognitoGuy.
BritishMormon is correct that communists would theoretically be allowed into BTA, as there is no rule prohibiting them yet, but I haven't seen any communists who have been recently active. I concede that it is misleading to say they would be "welcome" in BTA. They might be able to join, but other members would probably vehemently oppose their communist policies. You're right, BTA is not truly liberal, it's more of an anti-CTR party, much like CTL before it. CTL could conceivably lean to the left, as liberals like Slobama overwhelmingly oppose BritishMormon, but it is not exclusively liberal.