It's not always clear what is a "right" and what is just a socially encouraged preference. Do people have a "right" to keep their employer oblivious of their sexual orientation? Would people care about making it a "right" if they lived in a society where nobody discriminated on the basis of sexual orientation? If society is screwed up in such a way that enough people need to use workarounds to do innocuous things, at some point it might make sense to say that people have a right to use those workarounds.
If there were a single identity provider that supported multiple personas, and if it only exposed a persona of your choice and not your underlying identity to websites that used it (so that only you could associate your various personas with one another), and if this identity provider were highly trustworthy (preferably using cryptographic tricks to tie the provider's own hands), maybe it will be OK to ask everyone to sign in using that identity provider.
If there were a single identity provider that supported multiple personas, and if it only exposed a persona of your choice and not your underlying identity to websites that used it (so that only you could associate your various personas with one another), and if this identity provider were highly trustworthy (preferably using cryptographic tricks to tie the provider's own hands), maybe it will be OK to ask everyone to sign in using that identity provider.