Hey so I've actually looked into situations like this rather extensively because my parents have threatened similar on several occasions and I've used several different approaches to effectively combat this type of behavior. Here are your options:
A) Call their bluff. Tell them that you're an adult and you can do whatever you want. If they are Christian, tell them that it's a sin to judge others as you can only be rightfully judged on the eyes of God. As parents, their job is to accept their children for who they are as you accept your parents for who they are. If they try to kick you out for a medical condition that is recognized by the DSM-V (here's where I suggest showing them the DSM-V) that they are being corrupted by pride and that you will pray for them. When you call their bluff, you have to anticipate where they will draw the line. For my dad, it was when they threatened to kick me out of the house while we are driving down the highway and I more or less said "okay I'll leave right now" and opened up the door and unbuckled my seatbelt. I also made it very clear that I know both my parents' social security numbers, all of their credit card information, and every building permit they didn't file for. They often stop after I make my threats more extreme than theirs in a classic case of "mine is bigger than yours"
B) Agree, but set them up for housing discrimination (amazingly simple). Tell them you'll stop and like a week later say how you've been thinking that you want to help them by paying rent. Pay monthly by check and ask for a receipt with the excuse of using for a tax deduction or you can ask for some kind of informal lease by calling it a "written agreement". Make sure that in this "agreement" you make it look like it's completely in their favor that way if it's ever challenged in court, nobody will belief this was all your idea. After you've paid for a month or two, you can openly transition and if they try to kick you out, you are now a tenant and kicking you out for such a thing falls under housing discrimination. See, even if every state doesn't have laws protecting discrimination based on gender identity, they DO have laws preventing discrimination based on disability and asking you not to treat a condition recognized by the DSM-V violates the Americans with Disabilities Act and local discrimination laws. If they tell you they are kicking you out for that, record the conversation. Once you have a recording and a paper trail for rent, they can't even legally evict you because you have proof that they have ulterior motive.
C) Call the shelter and ask for a ride. Most shelters can assist you with transportation. If not, a lot of churches may be willing to give you a lift if you simply say "my parents have been emotionally abusive and have threatened to kick me out because of a pre existing condition". Make sure your language stays very surgical. If your explanation doesn't evoke an empathetic connection, most people will assume it's not something you want to talk about and/or it's been largely traumatic for you which has robbed you of an emotional response.
D) Last resort: call 911 and say your parents have threatened to hurt you. This is an outright lie and I don't recommend it. By law, if someone calls 911 and reports that someone they know is a threat to themselves or others, they have to be taken for a psychiatric hold. This depends on how well your local police force chooses to respond to said phone call and they could take your parents side. Ultimately, this doesn't achieve much except establishing that you are at risk as the police will be mandated to take a report which can help you get into a shelter more easily.
IF YOUR PARENTS CONFISCATE YOUR HORMONES, CALL 911. That is illegal possession of a controlled substance and that is at the very least a misdemeanor. You should browse through Tennessee penal law for the details on the law. The very threat that you will call 911 on them for a crime they would have committed will have your folks scared ->-bleeped-<-less.
BONUS: Again, if your parents are Christian, go to their church and speak with the clergy about counseling your parents to stop being oppressive, prideful, and judgmental. Most Christian sects are trying not to hate on queers since that hasn't been working out for them as of late. My local Catholic church states before every mass that everyone is welcome no matter what "orientation" (which is not the word I would have chosen but okay). If your local church isn't helpful, find out who presides over their church and just go up the chain of command. My dad wasn't open to therapy but when I suggested that he speak with the Father of the church he was much more open to dealing with our problems.
I hope this helps. You can also call places like lambda legal or the ACLU and ask for local resources. They will most likely be able to help you connect with your local trans community.
