The usual criticism of any form of the anthropic principle is that it is guilty of a tautology or circular reasoning.
With the respect to our existence and the Universe, the error in reasoning is that because we are here, it must be possible that we can be here. In other words, we exist to ask the question of the anthropic principle. If we didn’t exist then the question could not be asked. So there is nothing special to the anthropic principle, it simply states we exist to ask questions about the Universe.
An example of this style of question is whether life is unique to the Earth. There are many special qualities to the Earth (proper mass, distance from Sun for liquid water, position in Galaxy for heavy elements from nearby supernova explosion). But, none of these characteristics are unique to the Earth. There may exists hundreds to thousands of solar systems with similar characteristics where life would be possible, if not inevitable. We simply live on one of them, and we would not be capable of living on any other world.