Do gays have the right to be treated as straight?

Do gays have the "right" to be treated as straight?  And do men who self-identify as women have the "right" to be treated as female?

From Washington Examiner’s article:  “Unsatisfied, gays demand more from Obama”

Representatives of GetEQUAL and Students Working for Equal Rights told Secrets that they want Obama to take executive action to institute the Employment Non-Discrimination Act that is languishing in Congress. They said the act would protect employees of federal contractors from workplace discrimination based on sexual orientation and gender identity and that Obama was not taking the issue seriously.

If, as gay rights activists claim, sexual orientation and gender truly don’t matter, then why don’t gays simply orient themselves towards the opposite gender?  And why don’t men self-identifly as men?

It’s precisely because gender does indeed matter that we treat men and women differently. 

Treating men like men should not be illegal.

Gender matters.