It depends on your tolerance for risks with low odds. When you have had a vaccine that gives you 95% protection, that's pretty darn good! Just not 100%.
My understanding is that neck gaiters don't actually work, so there's that. If you're going to wear a mask, wear a mask. It has to fit tightly to work. Gaiters don't do that. I don't think the wiping is something to worry a lot about, getting covid from surfaces is a tiny risk, but in a gym people are huffing and puffing and putting a lot of droplets into the air. I'm not sure what the actual protection is from the vaccine you had, some reports put it at 94.7% or so from the earliest clinical trials and some put it at 90% now that folks are getting shots, and they are all less effective than that for certain variants that may or may not be around your community, so I would still wear a mask at a gym and if I ruled the world they would be required at a gym, but at some point we're all going to have to get back to life and accept a certain level of risk. How much we wish to tolerate is up to us, but again, because I believe in protecting others, I'd be more stringent in a gym than has been the case. I certainly haven't been to one, but again, can't stay hunkered down forever. I'd just want to see enough vaccine for herd immunity first, I think. Peace.
Do Wear a mask and urge others to do same. We are not sure of effect of vaccine on new variants