Wells seems more interested in society rather than class, but you can't have one without the other. They're peanut butter and jelly, people. In The Island of Dr. Moreau, society is a sham, a fake, an illusion meant to keep us happy. It hides the fact that we are animals, but it doesn't change the fact. The beast inside us can still come out at any moment. Just like the Beast Folk, our society is fragile at best and prone to break any day now. As for class, well, someone is always going to try and be on top.
The Beast Folk would have created a society with or without Moreau's help, especially after learning language. Moreau just used the power of language—i.e. the Law—to make sure he was on top rather than bottom. Why? Well, wouldn't you rather be in charge?
Montgomery finds companionship with the Beast Folk because he desires to return to society—any society, so long as it has brandy. This is why he ultimately helps Dr. Moreau.