It's really pretty simple in how I deal with them.
#1 - for most of them, the 1st time you talk with them, you'll NEVER convince them about what the good science shows for the safety and efficacy of the benefits of fluoride. They'll either have a few printed out pages of anti-fluoride anecdotes or quickly fire up their smartphones and pop to a few web pages with more anecdotal anti fluoride items. I just hand them one of the ADA printed info sheets that I have about the benefits of fluoride and the success that it has been in overall public health.
#2 - Coincidentally, I have noticed that many of the anti-fluoride folks tend to also be anti-amalgam folks, and even sometimes the anti-radiographs folks. This gives me a chance to talk some science with them, and often catch them off guard to the point where they stop for a moment just regurgitating anecdotal info they read on some webpage, and actually get them to THINK for themselves. If and when this happens (and it does in my office atleast about 2/3rds of the time), then I can have a rational conversation with them, about the materials that we use, why we use them, and what the pros and cons are with each one.
Once I can have a rational conversation with them (and for some I'll never be able to - those folks tend to get a dismissal letter after a few visits on the grounds of "difference in treatment philosophies") most of them, maybe not at that visit, but at the next one, will then agree to the treatment that I'm recommending, based on science and not fiction.
Much of it has to do with the basic difference in the educational concept that many people have vs. what we as dentists have. Dental school trains one (or atleast hopefully it does!) to CRITICALLY think about the data that is infront of us, and then based on that critically analysis of the data, make our decision. Many people, hear the data, and then without real critical thinking, make a reactionary choice, which often may not be a critical choice. That's what one often needs to keep in mind when discussing treatments with patients