Well, actually I could see a blend of different rationales. Doc wasn't able to see Gobo, and lots of people do seem to ignore Matt. However, Matt is able to order food, "steal" from grocers ... Also, people seem to come to his aid when he falls and such. Children also seem to accept his presence moreso than the adults. By the looks of that one episode where Matt mentions Halloween costumes, the Muppets are indeed popular enough to warrant Kermit/Piggy costumes. So, I would guess that some people are okay with Matt if they accept Muppet neighbors and such, while some people are "blind" to the non-humans around them. Even in the Muppet movies (the classic ones, anyway), Muppets are kind of ignored. Why that is, I can't guess. I usually interpret it in a Roger-Rabbit-kinda way, where Muppets, like Toons, represent any random ignored minority (it would also explain Kermit's constant Theater problems). In fact, (and this is just in general) humans only really seem to interact with Muppets if there are already some around (for example, Pete's already had talking rats before the Muppets showed up).
...
Now I'm confused ... I think I was getting to a point but my brain forgot what it was.