By "their own time" do you mean alone, at someone's house, after work? Or at their cubicles during lunch hour? Maybe the coworkers want to keep the workplace for work.
You're vague on what the "snide remarks" are, but if they're derogatory, he is also within his rights to confront her maturely, express that he would appreciate if she kept her comments to herself, and that this is a work place not high school and rude comments are inappropriate. Meanwhile, he could keep his flirting out of the office and remove the fuel for her fire.
If they're in the office when they trade sexually innuendoed massages, then technically it's sexual harassment, and any of the coworkers would be within their rights to file a complaint with the company. The boss was 100% right to put them on different shifts. The company would be liable for a lawsuit at worst, and an HR nightmare at best.
Some offices even have policies prohibiting office romances, and that if it's discovered that two coworkers are dating, one of them will be required to switch shifts, departments, or even locations.
For the record, no one can "make him" feel anything. Breathe is responsible for his own emotions, and if he can't handle being judged by people that live a different lifestyle, maybe he isn't emotionally ready to be so flamboyantly poly. I've read some of his posts, and I get a sense of insecurity, expressed as caring too much about what other people think of him.
“As I am sure any cat owner will be able to tell you,
someone else putting you in a box is entirely different
from getting into a box yourself.” —bisexualbaker