I was raised like this and find it heart warming to see funerals filled with wider community.
I did misjudge it once: I was living in a different country with two fellow Irish people and the relative of a good friend died. In Ireland it would have been expected that we attend the funeral, in this case we showed up and there were only six closest relatives there, and our presence just felt inappropriate. I now know your place at a funeral is about your place in a wider community. That often overlaps with being a connection-of-a-connection, but not always.
I refuse to believe for a second that your attendance was considered inappropriate; the person being burried at least would have surely been happy for you to be there and think of him or her.
Also, your intentions are to be commended regardless of what the relatives thought (it's not the relative's funeral, so they are not the yardstick).
No, different culture. That are many different cultures and OP made the common mistake of not understanding until it was too late that he was intruding on a different culture. Even though OP was in the wrong I cannot fault him for the mistake, there often is no way to know if you are not very close to the family what the correct culture is.
We had a similar issue. We ended up at a funeral for our daughter’s teacher (we brought the kids as she knew all of them), and somehow ended up in the family greeting line intended for close friends and family. It felt so intrusive and they were like “why are you here”.
The cherry on top was our youngest started getting restless during service and we had to leave early and we didn’t sit in the back.
I had only been to my parents funerals at this point, and never experienced a more formal religious service, but we were the worst in so many ways. I still regret it 10 years later.
I did misjudge it once: I was living in a different country with two fellow Irish people and the relative of a good friend died. In Ireland it would have been expected that we attend the funeral, in this case we showed up and there were only six closest relatives there, and our presence just felt inappropriate. I now know your place at a funeral is about your place in a wider community. That often overlaps with being a connection-of-a-connection, but not always.