If I was being transferred due to a transgression someone else did, I'd consider suing or leaving the company as a matter of principle. The outcome of a policy that involves transferring someone rather than dealing with abuse is you over time get left with those who are fine with maintaining an abusive workplace.
If someone is trying to force you to use a slur, they're being abusive. A pronoun is not a slur.
But again, being able to even have that discussion about what is and is not acceptable is a political discussion. That Basecamp has now banned.
I for one would never consider applying to Basecamp after this because they've made it clear employees can not safely discuss issues that may affect them at work.
More importantly, I'd consider a place that cared so little about victims of abusive behaviours a horrible place to work that'd be worth leaving regardless. I'd start thinking about leaving such a please even if I just observed it happen to others, because it says something about the lack of fundamental respect for employees.
Good point about a racial slur. But invert that. Should I be forced to call some by a racial slur because they are reclaiming the word if it makes me uncomfortable?
These are not easy issues. We are talking about the mutual rights of others and the ability to force people to act. A posture of good faith compromise is warranted.