I'm an Australian Scout Leader, I've been a Scout since I was eleven, and been avidly involved since, including doing a lot of international Scouting, especially very recently when another young leader and I cycled to Sweden for the World Scout Jamboree.
In regards to their discrimination policies, the BSA are pretty much outcasts in world Scouting. Sure, the religious thing is in our promise (though I've never heard of another country's national scout association having a policy against atheists/agnostics), but no one really cares what your religion is and nor should they. Interestingly, even on segregating boys and girls they are one of only a few countries left that openly do that.
I was fortunate to meet and work with quite a few great people from the BSA at the World Jamboree. The ones I worked with (Leave No Trace activity, we ran) were quite openly embarressed by these very BSA policies you mention. Not all the BSA is like that, though it will depend a lot on your troop. From what I can tell, Venturer Units, which are allowed to be co-ed, tend to be a bit more "open minded" though that is only my personal observations so far.
I wouldn't be subversive, just be a bit disappointed. Go to Philmont; I'm sure these policies will not come out to the fore in your experience there. Remember, Scouting very much is an internationally focused, open minded organisation, that promotes peace and understanding. There is nothing in that policy that says that YOU have to be a homophobe kicking out g.a.ys, etc. And if somehow something comes up and you don't agree with the conversation (this actually happened (!) with a bunch of old BSA leaders to me at the World Jam...) then politely state your opinion, maybe a few lines about how they are people too and can't help it, and then just move on away before it gets ugly. But I don't think it will come up anyway in your time at Philmont. Just be true to what you think the Scout Promise and Law means mate, that's the best thing to do.
The 2019 World Jamboree is going to be very interesting for BSA. I think a few minds in the organisation might be openened. There will be g.a.y and l.esbian scouts, scouts of all sorts of religions and none, etc. Sweden was amazing. There were large organised meetings for G.a.y/L.esbian Scouts (fantastic!), different religions, etc, etc. Scouts truly is a force for world peace.
Yours in World Scouting,