Here's one: female circumcision. At it's core, it is a quashing of female sexual desire. I don't care if it is normal in some parts of Africa, I disdain it and those who impose it. But it's not lost of me that I circumcised (well, not ME, a mohel) both of my sons and it was profound for me to publicly declare them Jews in the tradition of Abraham. There's a disconnect between my two points of view here. I'd love a logical connection, but I can't find one. One is ugly and disgusting to me; the other beautiful and profound.
I own a Keffiyeh. It's a traditional Arab scarf favored by Palestinians. It's not worn by women and it's not worn by Jews. I'm both and I wear it in protest. Well, let's be honest, it's comfortable, warm and attractive; that's why I wore it at first. But it's become a quiet FU to tenets I find disdainful. The treatment of women in many Arab countries disgusts me. I find burkas to be another way to hide women from the world and there are many Arab "cultural" actions I think are basically anti-female and they piss me off. I wear my so-called religious garment as a fashion accessory as a spit in the face of the misogynism that permeates Arab culture. As a Jew, I'm a strong supporter of Israel's right to exist. I'm confident that the so-called Palestinians (no such thing, really) just want to push us into the Sea. So again, my Keffiyeh serves it's purpose.
I wish I was more accepting. Who am I to make these judgements? Well, I'm me. And fortunately, I live in a free country.