1) The DM is a part of the group, so their enjoyment is equally valid as a member of that group. In other words, the group as a whole decides whether things need to change to make the group as a whole happy.
2) Yes. Players get to choose the characters they play, from a list of available options. In most D&D games, that list includes everything official, but not all groups do it that way. See 1) above.
Frankly, it is a DM's market right now. There are a LOT of people that want to play D&D and not enough DMs to go around. That means a DM has the ability to set their own boundaries and indulge their own preferences and then seek players that are willing to living within those. That said, I'm not sure what it benefits a DM to overly restrictive. There's a certain point where if the DM is trying to constrain what the players can choose for PCs, they are likely to equally constrain what the PCs can do and how they can act, and at that point the DM should be working on their novel.