Do you have family members or mutual acquaintances who could intervene with your parents? Because my instinct is that you shouldn't be dealing with this right after surgery and right after you've been diagnosed with cancer. Somebody (not you) should be telling your parents to back away - that this isn't the moment for you to be dealing with family problems. This is a moment when they should be supporting you through your medical trials.

Beyond that, it's hard for me as an outsider to grasp the best path, but if I had parents who had serious queerphobia, but I thought there was a chance that our relationship could survive, I'd enter into family therapy or some informal version of it that brought in a third party.

At any rate, the cat is out of the bag, so unless your parents share your view that silence is golden, it seems likely they'll want to follow up on these revelations.

(I'm writing all this without access to the comments that other folks are saying. I hope you manage to find some bits of helpful advice here.)