Yeah, the Boy Scouts are very religious in their methods. The oath even has you to pledge to "God and my country." I look back on it and sort of cringe a bit that I was being made to say that kind of stuff as young as I was and before I even had a real sense of what it meant. By the time I could have understood it it was just a set of words I had to repeat. (A lot like the pledge of allegiance when I had to say it every day in school, it lost its meaning completely to me until about high school where I declined to say it any longer)
I honestly wouldn't suggest it for anyone these days. If you want your kid to learn about outdoors and camping. Take them camping. They'll get more out of it that way than they will with the scouts.
Girl scouts may have changed, but most of the anecdotes I've heard relate to them being much more focused around cooking than anything else. Granted, all of these anecdotes are decades old.
I know there are some non-religious and co-ed groups that allow boys and girls to be in the same groups. They don't tend to have as large as a following as the scouts do though and many of them are limited in the areas they cater to, while almost everywhere has a scout troop or two.
Also, Vector. It was rarely that fun. Although a lot of it did depend upon the local leadership. Our group of adults was generally pretty lazy. They didn't do much at the meetings and the 3 or 4 campouts a year that they had, they didn't really plan any activities. It was just. We get there, set up the tents. They go off and do their stuff while they let us sit around and waste time. Around dinner time we'd all help gather wood and they'd start a fire. We'd all do something simple like roast hotdogs. (occasionally something a bit more complicated, but only had that happen once or twice.) After that, more wasting time till they told us to go to bed.
There was a regional thing every year that they took us to that was planned by someone else that did have some decent activities though. But even that was kind of underwhelming and they took so many pains to "keep us safe" that we rarely ever got to do anything beyond tying knots and walk on trails. A lot of the time, rather than doing something, we'd answer quiz questions from the manuals rather than prove we could do an activity, if we could quote the process, we'd be counted as if we could do it.
Despite all that though, if you wanted to do it, I feel you should have been able to. Just know that there really wasn't anything special about it.