My first religious service after coming out was not at a synagogue, but my first voluntary religious service after coming out was at a synagogue, and I'm very glad of it.
My late husband was Jewish, and we sometimes went to services together. He wasn't very religious, and I was surprised that the people at the synagogue didn't care about his personal beliefs or lack of them. What mattered to them is that he was part of their community.
A significant part of our social life revolved around volunteering for an event the synagogue sponsored, a monthly Sunday tea dance for LGBTQ elders. (All elders, not just Jewish people.)
I got to learn that Judaism as a religion is nothing like what I had learned as a Christian. Judaism concerns itself with this world, not a hypothetical afterlife. Judaism focuses on living out loving-kindness in a traditional Jewish ethical framework.
I'm so glad you mentioned that reaction, the observation that your parents are good people. That's a such a very Jewish thing to say, centering loving action, and not claiming anything approaching religious exclusivity in ethics or morality.