The Categorical Imperative is false because morality is based on hypothetical imperatives.

Are you suggesting that all of morality is conditioned? Because Kant quite explicitly differentiates between conditioned and unconditioned imperatives (in The Groundwork for the Metaphysics of Morals) (there's also a third: problematic or technical imperatives). The categorical imperative is unconditioned, i.e.: absolute, apodeictic, an "I ought to do" without any notion of "if", good in themselves without being means to further ends. But the hypothetical imperative, which Kant mentions, is of a different sort of imperative. It is conditioned, i.e.: it has this "if" structure and concerns only those actions which are goods as a means to an end that we will.

So the only way I can make sense of your claim is if you're denying that there is any moral action that takes the form of an unconditioned end. But that seems like a tough pill to swallow, to think that there is no or that no one has ever acted purely for the sake of duty.

Morality is a natural phenomenon, and it should be studied like any other natural phenomenon, by describing its nature and origins using observation. It is based on the fact that we have certain sentiments due to our nature that cause us to approve of certain character traits when we see people exercise them, like courage, benevolence, and empathy.

Kant also quite explicitly argues that experience does not justify actions as moral or good. Kant doesn't deny the empirical make up of morality, just that it isn't what makes it moral. The form of moral action itself (i.e.: like the categorical imperative) is where we need to look for justification.

Duty is a component of morality but it is based on our sentiments. When we see someone who has an impressive character, we sometimes dislike one or more of the character traits that we have and put forth effort to change them, which runs contrary to our ingrained dispositions. This causes us to feel like morality is being imposed on us from the outside rather than resulting from our innate sentiments and desires, but it is really just a result of our nature like the rest of our sentiments and desires.

Part of Kant's project in differentiating between the different parts of ethics was to avoid the problem of confusing duty with self-interest, which he argued would lead to disastrous consequences. You've seemed to have committed precisely the confusion he was attempting to avoid when argued that the nature of duty is determined a prior and not by experience or sensation. This is in part why I'm confused when you say this:

I think the Kantian approach to morality is dangerous for society because it condemns human nature, which might result in our organizing society in artificial ways that don't take people's innate sentiments and desires into account.

...since, firstly, one might argue that Kant's approach to morality was precisely trying to capture a part of human nature, i.e.: our participation in an intelligible world in which our will is naturally self-legislating, and secondly because its precisely the focus on sentiments and desires that posed the danger to moral action.