First of all, welcome to A2K. I hope you can stick around and continue to let us know about this 'Catholic Church-extremist propaganda and the link between MSNBC and transgender issues' issue. I'm making the popcorn right now.
I think she is referring to extremists propaganda not for Catholics but for LGBT side of things - in one way I agree with the sis about giving a child any sort of hormone treatment. Since (and of course this is dependent on the individual) most kids are still developing and changing both emotionally and physically - I honestly do not support any hormonal treatments and I do think that is extreme for kids. Different once you are an adult. To me teenage years are when you explore and determine what sort of person in all aspects you want to be... Personally I would suggest even waiting until after college age as I have seen my recent college graduate mature and change significantly since she started as a freshman.
One thing as another aside - as far as faith - similar you cannot force a child or young adult to have a certain faith. My younger daughter is just graduating from a Christian High School. It is a non-denominational Christian school whereas students come from various Christian faiths. One thing I did appreciate from the school's Bible teaching classes especially for the older students - they had them think, they had them visit a Christian Church that was different than theirs, the even promoted the fact that you as an individual need to determine your faith and it cannot be forced upon you. Parents/teachers/ministers can give you foundation, but you as an individual need to determine your own faith.
Your sister needs to do this. Yes you can teach her and encourage her in your faith, but she will ultimately determine what is right for her. And often times forcing something on her, scaring her (i.e. she will go to hell for being transgender) - will more likely turn her away from the very faith you are promoting.
Also, want to say I am sorry you are going through this - it must be tough to see your parents fighting this way. Do you have a counselor you can talk to at school? It might help you feel a bit better. It must also be hard for you to see your sister going through any sort of uncertainty. I just suggest you be there for your sister and let her know how much you love her. Remember too sexuality is only a small part of your sister. No matter what is determined later your sister is still the same person -- just focus on her relationship with her and be the kind caring big sister; my guess it is probably also tearing her a part thinking she is causing this rift between your parents. Letting her know you care so much about her and love her no matter what will go a long way.