The trick to compromise is the age-old improv trick: don't say no, say "yes, and..." More forcefully, "yes, but..." When absolutely necessary, "no, but..." Rarely should you say straight-up no. Inform them of exactly what the consequences of their choice will be. "You want to pelvic-thrust the stone wall? Fine, roll me a strength check. Good job, you broke your pelvis on the wall." "You want to turn the king's hands into dicks? His court wizards will be able to trace the spell back to you. Are you prepared to accept this risk?" "You want to skull-fuck the bugbear corpse? Your penis gets stuck in the eye-socket, and tears open as you try to pull it out. Take 5 HP damage."

Alternately, if you absolutely cannot work with something, i.e. cat people, give them an option they might like. Presumably, cat people are meant to be Skyrim's Khajit. Tell Sally about how Elves have pointy ears and darkvision, and are light on their feet, and maybe suggest that she could have been magically transformed to look like a cat person? Now you're mechanically playing with an Elf, and Sally can meow and tail flick to her heart's content.

As for the tone thing, that's up to you. The tone of the campaign is determined by what you make happen in the world, more than what the characters decide to do. In the campaign I run, the Session Zero was a fairly-standard dungeon crawl, which I played off as the midterm exam of the Adventurer's College they were all attending. It was lighthearted and jaunty, full of jokes and epic feats. When they returned to the town, however, its gates were barred and no one was manning the guard towers. They got into town over the walls (the rogue had a grappling hook), and saw that it was mostly abandoned. The druid set his pet pigs loose to look around, hoping that they would return running from whatever danger there was. As the party walked down the street, I slowly described the town in more ominous terms. Eventually, one of the druid's pigs returned, limping. As it got closer, the party realized that this wasn't the limp of an injury. This was the puppet-like shuffle of daemonic possession. And so, the druid had to kill his own pet. The next session, they stayed out of the city altogether, and began building a fort to serve as a base of operations to eventually retake the city. The tone is what the DM decides it will be. Trust me, one of my players is every bit as That Guy as your friend Bill. However, even he grew somber when a corpse fell out of the closet that had obviously been barred from the outside.