I've had those same questions and have been advised that most of the masks on the market are to deter you spreading any viruses to other people. I would suggest you carry a small bottle of sanitizer with you and use that. Get a mask that can be gently washed or rinsed daily.
Recent information is that the problem is not so much someone touching the front of their mask as it is them then exposing their nose and mouth to the general air supply while their mask is off their face, breathing without filtration. (Including blowing one's nose, unless they are the world's best tissue user and catch every atom in their Kleenex.) The evidence is just getting stronger and stronger that Covid is spread by breathing in the virus floating in the air, and with the new variants there are a lot of those, not by touching things. This would include our masks, although if fresh virus is on the outside of the mask it would be a good idea not to dislodge it and cause it to float into the air by handling the front of the mask. Basically, Covid is a disease with respiratory spread. A mask is to keep from breathing it in and getting sick, and from breathing it out and making someone else sick.