It sounds like it is normal getting asked if you have pets. but is not. They just could tell you not to have a dog, cat or whatever. But it is not their busines if you have snakes, spiders or a normal number of guinea pigs. And also it is not their job to judge someone because a shaved head and driving heavy motor bikes only because there is a housing shortage.

If there wouldn`t be a discrimination and racism act, advertisement would probably look lik this.
Apartment to let:
To a friendly good earning person in higher position. No foreigners, no pets at al. Likes to stay over the weakend in St. moritz. Not maried, no kids, no musician. no hyperhidrosis of feet, medical assessment required, no smokers and tenant should not be at the rented place as much as possible, there is an attendance recorder etc.