Are there triclosan-free antibiotic soaps?

Yes. Search the internet for specific triclosan-free soaps. Or you can even ask your doctor for specific handouts and recommendations where to find this information. Tru-test can also be used for information.
Yes, sort of. Soaps without triclosan are "antibacterial" because washing with soap takes the dirt & germs off of one's skin, rinsing everything away with warm water from the faucet. Adding triclosan doesn't give additional benefit over using plain soaps, but does send a lot of triclosan chemical into our environment. If "mrsa bacteria" is causing infections, a doctor can give special instructions on bathing.