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I'm sorry to hear your family is like this. It isn't right that they aren't willing to accept you or other people based on their religion. There may be support groups for LGBTQ+ individuals online that you can join. Check out one of the resources we have called the Trevor Project. They even have a social media platform, Trevor Space, for people aged 13-24, to meet other people in the LGBTQ+ community. I don't think it lets you join if you are over 24, though. There may also be groups in person but I understand that you don't drive. I don't drive either and it can be tough to get there! There may be bus routes that you can try.
Using new pronouns online can be a great start! Use whichever ones make you most comfortable on TeenHelp and other sites.
I usually buy my clothes online. It may take trial and error to find clothes in the right size, though, if you go this route.
I would wear the sports bra for starters and then add layers from there. For example, a tight-fitting (but not restrictive) undershirt or tank top under the T-Shirt you are wearing. I looked online for more tips and they said baggy clothes might not actually work well because it can cause shadows or hang off your chest and create more curves where you don't want them to be. It also suggested using darker colors/patterns.
Do you think you can pull your hairdresser aside and explain your concerns to them? They've probably seen a lot of different requests in their time and might be able to accommodate you.