I don't think grandparent was equating them, but rather pointing out that someone in a position of power could one day equate them. If the rule is going to be "your website only exists if one of a handful of powerful people don't veto its existence," then you have to worry that one of those powerful people would someday decide that LGBT advocacy turns his stomach in the same way that Daily Stormer pissed off Matthew Prince.
If, on the other hand, the rule is "your website exists as long as the courts don't decide otherwise," then both LGBT sites and Nazi sites are safer.
LGBT sites are pretty safe because there are anti discrimination laws that would enable a lawsuit with a high chance of success when discriminated against for that reason. Good luck trying to establish Neo Nazism as a protected class under the law.
If, on the other hand, the rule is "your website exists as long as the courts don't decide otherwise," then both LGBT sites and Nazi sites are safer.