I’d like to read about how LGBT+phobia has been in the US and how more recent stuff like straight pride and TERFs began to develop. Is there a book or something that talks a lot about this?
I feel somewhat qualified to give you a list of books on gay history, which contexualize the persecution of LGBTQ people quite well. All books listed are scholarly and include comprehensive references. I am currently an undergraduate student focusing in LGBTQ history and public health. Mods, if this is inappropriate please let me know (and sorry in advance!)
GayLaw by William Eskridge - a overview of the US legal system and the systematic criminalization of LGBTQ folks. This covers the 19th and 20th centuries, mainly, but offers prior context as well. Eskridge has also written other texts on the subject which are worth picking up. This book quantifies and contexualizes persecution using a legal framework and seems most directly related to your query.
A Queer History of the United States by Micheal Bronski
The Gay Revolution & Odd Girls and Twilight Lovers by Lillian Faderman. Her other work is well worth reading, too.
The Stonewall Reader from the NYC Public Library and Stonewall by Martin Duberman are worth picking up, too, even though the focus is much more narrow.
Queer (In)justice by Mogul, Ritchie, and Whitlock
Transgender History by Susan Styker, for a trans specific overview.
These are the texts I am familiar with, though I am sure there are many more quality books on the subject. While they are not overtly about LGBTQ+ 'phobia,' it is implicit in any historical account and certainly enlightening. I am following this thread now in the hope that someone more qualified will chime in!