It is not even that scientists disagree with the anthropic principle, but rather that they disagree about what the significance of it is. It is true that the universal constants are would need to be in order for human life to exist. But many scientists respond to this fact by saying “so what?”. If things were different they wouldn’t be the same. If they were different perhaps another form of intelligent life might be here considering a similar ego-centric concept (but likely not), but so what? Consider that the universal constants are exactly what they would need to be for the cockroach to exist. This is absolutely true, does this mean that the universe was designed for cockroaches? I don’t think so, but the “roach principle” is just as valid (and just as invalid) and the anthropic principle. Also consider that the universal constants are what they would need to be in order to create maximum number of black holes in the available space. Does that mean that they were designed to create black holes? Again I don’t think so, it is possible that some grand entity out there wanted a maximum number of black holes, but there is no evidence of this, and no good reason to think so. And there is no good reason to think that the universe was designed for humans either, other than human egotism.
To sum it up, we don’t really understand how the universal constants came to be what they are, we really don’t know if they could have been different (or how different), and we certainly don’t know why they are what they are (we don’t even know if there is a why). You may choose to assume that they are what they are for the benefit of humans, or you choose to assume that they are for the benefit of cockroaches, but we don’t know that. And whatever assumptions you choose to make, your assumptions are not evidence of Intelligent Design.