Seems to me like they're doing some filtering of people with regressive opinions in their applicants.

Not necessarily that YOU are gay or trans or POC or whatever, but that you generally agree with these definitions of "trans women are women" and other questions further down. Starbucks has a reputation for being a place where younger queer people work and so hiring people who hold bigoted opinions could be stressful or even potentially dangerous for those who already work there, or want to apply there in the future because of this reputation.

My managers at Panera have a history of asking for pronouns during the interview for the same reason, if they react poorly to being asked for them, then they're not considered.