In my experience, male bonding occurs mostly in hard times. I've been to war, been homeless and been to jail. It was in these times - be it a battle buddy, cellmate, or another guy on the street, that bonds were forged. I just watched that movie The Perfect Storm and I thought that had a good example of this as well.Throughout my life secular friends were always better than "Christian" friends. In all churches I visited, save two, the men were effeminate, indecisive, pacifistic and not respectable. Whenever I spend too much time with those "men" it turned me away from God and lose the masculinity I finally build up. The only good things about them were their reliability and knowledge about their faith, but knowledge and church attendance does not equal virtue. The deepest bonds were with secular friends, specifically from Muslim countries, be it secular or devout Muslims, I got along with them better than with my "Christian brothers". This extends to Far-East Asians as well. With the people of my blood and faith, I share nothing in common with. If you are weak in virtue and brittle in character then the Satanic Globohomo spirit takes hold of you.
Only in the Syriac and Coptic Orthodox Church have I seen strong bonds and real men, needless to say I spent a good deal of time with Arameans.
At this point I keep secular friendships transactual; one hand washes the other. There is no reason to be attached or expect anything deeper. As Edmund Hulse said: There are no friends, only business partners. And in a more atomized world it rings truer than ever.
Have you heard of the 80-year-generational-cycle? I think there's a lot of truth to it, that every four generations society flips, based on hard times create strong men, strong men create good times, good times, good times create weak men - repeat. Historically, the west had its last hard times in the 30s and 40s (Great Depression, WW2), and its peak of good times probably from the 80s into the 2010s and is hitting its hard times again now.
If so, that obviously sucks in a lot of ways, but it would mean we could see people making deeper bonds than in those good times.
The trick is to try, even when the world around us is having hard times, to have our family and community to have some sort of good times, and to not let those good times get us complacent on the importance of making strong meaningful relationships.