Direct Opposites:
* Reject: This is the most direct opposite, meaning to refuse to support or approve something.
* Condemn: This implies strong disapproval and criticism.
* Disapprove: This means to have a negative opinion of something.
* Oppose: This means to actively work against something.
More nuanced antonyms:
* Criticize: This implies finding fault with something, which can be seen as the opposite of endorsing it.
* Denounce: This implies publicly condemning something, which is a stronger form of disapproval.
* Refute: This means to prove something false, which can be seen as contradicting an endorsement.
Other possibilities:
* Ignore: This means to pay no attention to something, which is the opposite of actively endorsing it.
* Disregard: This means to treat something as unimportant, which can be seen as the opposite of endorsing it.
The best antonym for "endorse" will depend on the specific context and the intended meaning.