How does a Christian deal with discrimination policies at the workplace that forbid discrimination or even making people uncomfortable on the basis of religion or sexual orientation? Is it a compromise of Christian witness to submit to this?
I would say this compromises your integrity only if you intend to be "demeaning, abusive, hostile, insulting, embarrassing, sexual, or intimidating" (quote from one such policy) to co-workers as you testify to them about Christ. You shouldn't be these things to witness faithfully to Him. There are times it may/will get intimidating for them. Save those encounters for when you have them over grilling on your back deck, instead of at the office, and you're fine. This is not selling your soul. It is practical sense: the company doesn't want disruptive conversations making volatile relationships, hindering productivity. And you need a longer, more private setting to get really into things, anyway.
Yes, they are misguided regarding not discriminating according to religion and sexual orientation, and yes this is a subtle form of persecution. But they are doing that due to a generation or 3 of corporate compromise on the part of the Church in its cultural engagement. It can't very effectively be taken on IN the workplace - cultural assumptions must change back, first. Consider that we are like Israel in the book of Judges, now, oppressed by Midian. We need a Redeemer (Boaz), a prophet (Samuel), and a king (David) for things to start turning around and to beat back the Philistines. I'm not saying don't question it, but be realistic about what will or will not happen when you do.
We also need to put some thought into what the crown rights of Christ in the public square looks like for the homosexual, pornographer, Muslim, etc before Christ returns. Should unbelievers be second-class citizens, as far as rights go? Not all sins should be crimes.