I don't think you're being unreasonable. Too many people knowingly infect others with their germs and it bothers me to blitzes just like you.
Your body is a temple and you are in charge of your care. I don't see what the big deal is as long as you are getting your exercise routine at home.
I just got a cold as well, started yesterday. A relapse for me started a couple of weeks ago but getting sick has put me flat on my back so I understand how you feel.
Rest up and feel better.
I do agree with a one finger solute though