Easy , you tell them out. Mamdani used the party and has become a Trojan horse. He doesn’t care about NYC . It shows with focused arresting Bibi. The next day two Jewish people were attacked and he has said nothing,
Telling them out doesn’t actually prevent them from filling and running. There’s no shortage of people telling them off (including, as you pointed out, the former DNC chair), they can file as Democrats regardless.
Apparently some liberals, whether they consider themselves Democrats, DSs, or something in between, don't want to win elections. WTF is wrong with these people? The Democratic party is changing, shifting to the left in just the same way the Republican party has shifted tothe right. That's politics.
The DNC nor state parties have any role in accepting or rejecting candidate fillings. Secretaries of state do so.
Parties who have gone to court to try and get someone off their primary ballots typically fail (see Dan Sullivan in Alaska for a similarish situation).
I'm more concerned about ending the practice of shuffling 'troublesome' men, be they candidates, electeds or staffers.
Maybe we should get rid of the predators before turning on each other?