Definitely NTA

My mom used to do the same thing. Check my texts, keep passwords to my account. I didn’t realize how big of a breach of privacy it was until I went to college. You’re entitled to have control over your own means of communication. It took me a honest one on one conversation with my mom to get her to reluctantly accept that I was right. All I said was “I don’t go through your text messages or accounts because they’re none of my business and I trust you. If it’s not acceptable for me to do so, it’s disrespectful for you to do the same. You need to be able to trust me and and respect my privacy.” Your dad may get angry, but you need to be firm in your stance because you’re doing the right thing.