Without a fever or other obvious signs of illness such as diarhhea, I would still go to a birth. Have done so--when feeling like I may be coming down w/something, or just getting over something. In this case, I make sure to take excellent care of myself during the birth (resting when possible, eating right, using supplements/herbs if called for). I also do a LOT of hand washing, and just try to be extra super mindful about germ transmission...more than usual!
Last winter, for instance, I had a pretty bad respiratory flu with a cough. First, I just laid around for a few days, pumping the vitamins and herbs, resting up since I had people due soon. When the births came a few days later, I felt much better but still had a bit of a cough. So I made sure to keep tissue on hand--when I felt a coughing bout coming on, I would grab tissue and try to get out of the birth room before coughing (at least as far from mom as I could). Cough into the tissue, then wash hands. I also brought extra clothes, changing them more often than usual.
I had 3 births in 30 hours...neither moms nor babies got sick. But again, I was feeling much better, no fever, cough was present but reduced by then. No way I would have felt ok going to those births during those days I lay on the couch sipping soup and ginger tea, coughing a lot, low fever, otherwise fatiqued!