If I understand you correctly, by turning the argument around (against LGBT, atheist, liberal, etc. people) you want to challenge my point that it is okay to criticize and resist certain opinions and draw consequences from them.
I feel like there is a big difference between the scenario at hand and systematic persecution of certain groups of people.
You seem to assign a huge value to keeping a job. Do you think this is equal to being tracked down and killed by police? That's what e.g. LGBT people face in some countries, is that what you mean by that?
From my point of view, that employee actually tried to advance a very hostile political agenda with what he wrote, that might have harmed many people. Of course, this harm is not as visible as being fired, but it does hurt the opportunities for women, who have to try twice as hard in an environment, where you need to fight with people over whether you are even biologically capable of doing your job.
On the other hand, following your example with the guy making pro-LGBT statements: you make it sound like LGBT is some sort of political agenda by itself. But people usually just _are_ lesbian or trans without making a huge fuss out of it… I do not see how this compares to writing a 10-page essay systematically attacking half of your co-workers.
And, no, I would not defend Google for firing somebody for, say, being a lesbian. That's a completely different scenario.