I see the reductionist attempt to equate the two, and sure they have in common the fact that it involves people moving their bodies to a new location, but that's where it ends.
Not a single person I know, not even the most liberal, border-erasing people would advocate for the complete eradication of property rights, nor for the removal of a property owner's choice of who to allow on said property.
As a conservative, I was sickened by the filing, because if even half of it was true and not taken out of context, it indicates that Google does have an institutional bias against certain ideas being tolerated.
I'm not saying people should be allowed to harass others, but some of these reactions would constitute harassment.
FWIW, I think this is really an issue of many people at polarized edges of an ideology aren't able to have a constructive discussion without it devolving into shows of force to silence the other.
No. I can change my religious affiliation, my choice to engage in collective labor activism, and choice to engage in political activities. The first two are federally protected and the all three are state protected in California in employment.
Immutability, or even not being a matter of personal choice, have nothing to do with labor protections. In fact, labor protections are often about freedom from coercion on matters of choice.
(Not, of course, that the usual concept of fluid gender is that it is a matter of choice or subject to personal control.)
On the contrary, opinions like religion and politic affiliation are the exact opposite (and that you find those conflated in things like CoC troubles me).
However, that brought the interesting distinction about differently protecting traits that you can just decide to change, versus those you were just dealt with and are immutable part of you.
So gender is misplaced there, fluid but not so much a choice. However, the question as posed seems still valid to me for opinions : religion and politics.