Question about dependant coverage

I am a (soon to be former) dependant on a family Anthem BCBS plan. I’m getting a surgery 14Dec2022 and my coverage ends on 01Jan2023 because my parents found out I am getting sterilized and they are religious so they’re cutting me out. Thats entirely their decision, but it actually looks like I’ll be covered until 01Jan2023 as per the end of coverage letter my old insurance was able to provide me so I can get insurance with my job. My question remaining is this:

Can a policy holder ask the insurance (somehow) to withhold coverage of a specific procedure because they don’t agree with it? Under their plan right now it would be covered 100% but they read my mail (though I live somewhere else, they send all information to the policy holders address which they assured me they wouldn’t do, but then they did and insisted it was their policy, hence my parents found out and I dont trust them, etc). Could they appeal to Anthem or whatever and ask them to not cover my procedure so I’d have to pay out of pocket, or can insurance not deny a dependant coverage of a covered procedure until their coverage ends? I spoke to several agents about this but I don’t trust their answers due to past experience of them assuring me my info wouldn’t be available to my parents because of my age (24) and the fact that I live apart from them. My parents aren’t bad people, they’re just religious and want no part of this and would rather me pay out of pocket than have anything to do with covering my surgery. I have been waiting for this for years and it took me about 6 months to get scheduled for this surgery so I’m being stubborn on my end and not rescheduling. Can anyone help me out with my question?

Tldr: Can a policy holder ask the insurance (somehow) to withhold coverage of a specific procedure from a dependant because they don’t and their depeandant to use the health insurance “for that”? Or does the insurance have to cover it?