Technically you should be able to get a GD letter from a psychiatrist, and start hrt too, without parental consent if you're an adult.
But practically this depends on your psychiatrist. Dr Shiva Prakash, who's a trans friendly psychiatrist that's often mentioned here (I got my letter from him too) denies the letter to people that are financially dependant on unsupporting parents.
You could try other doctors though.
Or make sure you're financially independent enough/ seem financially independent.
