If the passenger next to you has a cold then, no, the FA will not remove them from the flight for health reasons. That pathogen has probably already been swirling liberally around the airport and planes for days anyway - you just happened to be next to someone who was visibly symptomatic. If they're coughing up blood, puking or have the trots then that's a different matter. Sickness tends to evoke a strong reaction in others, so if you are feeling uncomfortable about sitting near someone sneezing then that's basically your problem. Deplane if you want to - it's your right.

I was once on an internal flight in India where a gentleman two rows ahead of me was a bit short of breath and kept rubbing his sternum. He said it was because he had to run to catch the flight but the FA removed him because the pilot didn't want a heart attack to deal with in mid-air. If the shortness of breath didn't bring on the heart attack then I'm fairly sure the apoplectic fit at being deplaned was a strong second candidate.