During session 0 I explain how "abnormal" characters are handled. For example, half-orcs are hated and feared among almost every single civilized area, but I've changed their appearance back to the 1E version (10%, including all PCs, can easily pass as an ugly human). Drow would be killed on sight, so they should disguise themselves (assuming I allow drow in the first place). If someone were to find out about the abnormal character, the PC is going to be in a lot of trouble, and the group as well for traveling with such a foul creature.
I've not had the issue of a dangerous animal companion entering towns. Usually the player will simply choose to remain outside of town, or at least instruct the animal to remain out of town, and if I know I'm going to have such a character in my campaign, urban adventures will be limited or non-existent.