I discovered small diamond hole saws a few years ago. (Milwaukee Diamond MAX or similar, starting at 3/16".) The SWMBO likes to get decorative flower pots, but some of them lack drains or the drains are plugged with glaze. The hole saws make quick work of adding drainage without shattering the delicate crockery.
Do find a spare tile to practice on. I start with the drill tipped slightly and a very low speed until it creates a groove, then slowly square the bit up and increase the speed. (The start is so slow that I can use a finger against the side of the bit to keep it from "walking".) A little water for coolant improves the lifespan of the bit.
The diameter of the bit should provide a clearance hole for the screw, i.e. slightly larger diameter than the O.D. of the screw. (Hole saws tend to make slightly oversize holes) Stop as soon as you complete the hole through the tile, bedding and backer board and switch to a standard twist drill for the smaller pilot hole in the stud.
The risk of cracking the tile is largely a matter of whether there is a gap between the back of the tile and the framing. It ought to have backer board installed tight to the framing and the tile bedded without gaps. There is no need to overtighten the screws, just run them down until they're snug.
NB: Don't forget to caulk thoroughly during installation. Water in walls is evil.