Since when is HRT the only sort of progress towards transition? Quite frankly, hormones are over sensationalized not only in this subreddit (no offense y'all) but by pre-transition TS women everywhere.
What are you going to do after you get on HRT? Magically start living life as a woman because of some pills you'll take everyday? Nope.
So what you should be doing imo is stop focusing on the negative and bloom where you are planted. You're lucky to have understanding parents who are at least willing to work with you on this because it seems like they're worried about your social standing and not you actually being trans. Actions speak louder than words, so show them what you've got.
Start growing your hair out all in one direction. Start grooming and styling it daily either with a flat iron or curling wand and at least one styling product.
Do your nails and maybe start wearing acrylics.
Re-do your wardrobe and go with your mom and siblings to try on women's clothing and invite a sales assistant over to tell you how you look just so your mom has to sit there and listen to you be complimented on how pretty you are so she can SEE first hand "oh this is what people are gonna say/think".
Bribe your siblings if you have to but make sure at least one of them is commenting on how pretty you are in front of your mom.
Work with the therapist to get to the route of their fear of you transitioning.
And BEGIN HAIR REMOVAL. NOW. THERE IS NO SUCH THING AS TS WHO SAID "I wish I'd waited later to start hair removal." NOOOO GO RUN GO NOW. If your parents aren't wiling to budge on the HRT thing then ease in with hair removal using positive NLP words like COMPROMISE and STEP FORWARD but avoiding words like PERMANENT or IRREVERSIBLE.
Then when you've actually started making steps and strides you'll realize that getting HRT hormones isn't hard if you have a credit card and to top it off you'll actually be living fulltime as a woman anyways which correct if i'm wrong but should be the goal of any TS hormones or not.
You might get to a doctor and find out some rare liver condition makes you permanently inelligible to take drugs of any sort- are you really gonna put your life on pause waiting for magic pills or are you gonna make this moment count?