Is it safe to ride while taking mucinex (guaifenesin)?
Plain old Mucinex (without the "-D" suffix) is guaifenesin, one of the most innocuous drugs in existence.  Unless you have a peculiar (and rare) reaction to it, it should be about as safe as one can hope for.  In fact, I'd recommend it if you ride in dry or dusty conditions.

Mucinex-D, on the other hand, contains a decongestant that can cause drowsiness and other such symptoms in a substantial minority of patients.  (And I believe it can also be picked up in pro sports drug tests.)  You should take that while riding only after you've established that you don't react to it (and you're not in pro competition).

Also, of course, if you find yourself getting congested on rides that's a likely sign that you need to drink more water.