My grandparents were the same way. It seemed as if they operated on the logic that if they just spent time with me and firmly refused to affirm my gender identity, then I'd just grow out of it. I ended up cutting them out of my life, and their literal response was "What if we just agree to disagree and not talk about this subject at all?", and then I highlighted that being impossible because of the real-world differences that they'd have to handle, "What are you gonna do when I start looking feminine?", "What are you gonna do when I ask you to stop deadnaming me?", "What are you gonna do when my voice changes?", and when I asked them these questions, they ended up explicitly affirming that they are not going to be comfortable with these things. This gave me two possible conclusions:

• A) They think that they're not going to have to adjust to these things because I'm not "genuinely trans" and that I wouldn't be serious about my gender identity enough to proceed with these things. This is a plausible conclusion because they, as staunch Catholics, have explicitly said that they don't believe that LGBTQ+ people exist.
• B) They think that their suggestion of "just shut the fuck up about it" will make me not care about the subject anymore, in an "ignore it and it'll go away" kind of fashion.

Either way, the outcome is that I cut them out of my life so that they would get the memo that this is a non-negotiable situation. You can't have your cake and eat it too. Want to be transphobic? Okay, then get the fuck out of my life. Want to be in my life? Okay, then stop being transphobic. Want both simultaneously? Sorry, my boundaries don't permit that!

They were so disingenuous that they said, "So simply because we don't perfectly agree with you on this subject, you wanna never talk to us again!?", and it's so bad faith because they're constantly trying to phrase this as a matter of opinion, opinion, opinion, just fucking "opinions", without regard to the material implications of said "opinions". This highlights that they view this matter on a completely false premise.

I disagree with them on a lot of subjects. For instance, my grandparents are staunchly opposed to abortion to the point where they're practically single-issue voters around it. They wouldn't dare vote for a candidate that's pro-choice. However, despite this, I never considered cutting them out of my life over their views on abortion. In a hypothetical alternate universe where I'm a pregnant cis woman who wanted to undergo an abortion on the other hand, having to deal with my grandparents being the same degree of anti-abortion as they are in this universe, I'd have to cut them out to properly go about my life, and that's the key difference: real-world impact.

Transphobic family members are something else, especially if they're religious.