I see this comparison a lot and I want to point out exactly why it’s false:

We oppose discrimination against protected classes because generally we recognize that people cannot elect into or opt out easily of those classes. It’s generally greed upon that people do not choose to be gay.

Parler’s users choose to post white supremacist content.

I see no contradiction in insisting that gay people be served under the law while advocating that private companies retain their right to refuse service to White supremacists.

The Supreme Court has backed this up: discrimination on the basis of sex, which includes sexuality, is illegal, while discrimination on the basis of political ideology is not.