Thank you very much for providing this additional information, Alex.
It sounds as though you could pursue a charge of discrimination
based on sexual preference, but as it appears you are not interested in doing that, there would typically be little recourse against the actions the employer is taking against you.
Signing the PIP document will not usually indicate that you agree to the facts stated in the document, but only indicate you have reviewed it. You could even make a notation on the document that you do not agree with the facts contained in it before signing it.
It is impossible to hit a moving target in many cases and the company may know that and be setting you up for failure as you suspect, but without pursuing a claim of discrimination, they would normally have the right to make such decisions about your employment including termination
As far as unemployment though, unless they can prove there was good cause to terminate you, you would typically be eligible for such benefits. Performance issues do not typically rise to the level of good cause so unless you intentionally violate some law or employer policy, you should normally receive such benefits.
With regard to severance, if the employer does have a practice of paying severance, then you could pursue payment for that if you are terminated based on an implied contract theory of law. That could be pursued in small claims court or through the assistance of a local attorney.
I hope this helps clarify the situation for you. My goal is to provide you with excellent service – if you feel you have received anything less, please reply back as I am happy to address follow-up questions. Kindly rate my service when I have answered your questions so I will be compensated for my time assisting you. Thank you!