I found grandmother is Jewish but my lifestyle might affect this

Hello, I recently found out through family documents that my mom’s mother is Jewish. She was a Hungarian Jew. I knew Jewish was passed through mother from a friend. I would like to connect with this part of me, but am wondering if me being gay and having tattoos affect this. I recall hearing that Jews can’t have tattoos?idk I came to ask this no offense.thanks!(I was not raised Jewish)