I am also against transphobia. You can care about multiple things, it isn't either/or. There are indeed fat trans people too. And respect and love given to someone else doesn't mean you can't also have it.
Actually, I'll elaborate on this and we will see where it goes.
Abusers are intersectional and thus the abuse victims receive is intersectional, as it is projection. Abuse requires little-n narcissism. People can be narcissistic about certain things, which cause delusions that are literally inflammatory and agitating. These delusions inform the "type" of narcissist, who needs confirmation for the delusions (called narcissistic supply) to soothe the inflammation reality provides when their delusions fail to match.
Narcissists with their friends or family who are enforcing delusions and getting supply as a condition of their relationship are known as abusive relationships. Narcissists grouped together in large bodies are known as cults - abusive interpersonal dynamics scaled up. Narcissists grouped together for the purpose of political movements is fascism.
Another name for transphobia is gender fascism. It is directly related to cults (eg Christofascism) and interpersonal abusive relationships. That dad sending you nasty messages is probably some transkid's abusive dad. They look for people sensitive to their abuse (usually with a history of same type of abuse) to inflict narcissistic abuse on, because the distress of their victim validates the delusions and gives supply.
Another name for ableism is physical narcissism/physical fascism. Controlling other people's weight with shame and abuse etc is an example. Projecting feelings onto them about their weight being disgusting or bad is another example. Making up a narrative that fat people's existence and acceptance means transphobia somehow is worse is a delusion. It may feel comforting and give supply, but it's not real. It's a story.
One person may not be a physical narcissist, but a transphobe, and vice versa. Someone may be neither, but a racial narcissist. Narcissism isn't a disease, it is a belief set btw. It is as contagious as hearing the word of God or seeing a meme, because it is a belief set.
What you likely crave is freedom from narcissistic abuse. Rec book Stop Caretaking the Borderline or Narcissist, can be used on your self to help with narcissistic thinking habits that create delusions. Our entire society is narcissistic because advertisements inflame them and so do cheap shitty shows like Tucker Carlson etc. If you have cPTSD, that is on the dissociative spectrum with borderline personality disorder, often caused by narcissistic abuse. Unlearning and disagreeing with narcissistic belief sets will improve/treat your cPTSD if from that.