These laws were changed in ~2018 in Austria.
That's one way to implement it, one can come up with many others.
If you view the world from the point of view of [rights I have] vs [rights I don't have], you may as well be a happy pig in a cage. This worldview is in fact fascist, because it implies that the state should "give" you rights (giving you this type of right means taking away someone's freedom).
The opposite view is giving you the freedom to do anything as long as you don't attack someone (physically) or steal from them. If you want to prohibit something you must have good reasons, not "let's give everyone rights" or "it makes people feel bad".
Having a "right to not be insulted" means that you don't have the freedom to insult. i.e. you have no freedom of speech. If you put emphasis on the "right", you view the world like the pig in a cage, if you put emphasis on the freedom side, the opposite.