If your manager pushed you out because you are gay, that is discriminatory. I'm truly sorry to hear that and I hope something is done at LinkedIn so that environment is changed.

However, there are usually two sides to a story. I hope you are also considering the possibility that it had to do with your work, your work ethic, your ability to work with others, your ability to take direction, etc.

Speaking as someone on the other side, I hate PIPs too as well as the institutional performance review processes. I wish I could get rid of low performers easily but it is pain.