Excellent article, Joe. I've added some thoughts, which I hope will add to this theme.
The idea of something bigger than yourself is thought to increase your own importance or significance. Instead of just being one more person in the world, you'll matter. Your impact will be magnified by the cause. By attaching yourself to something important, that importance rubs off on you.
I suspect that is very true for many of those who join, but there are others with a different motivation. Some don't even look to increase the meaningfulness of their life and they aren't an activist, so they don't expect to make an impact or to be more important. Instead they want to feel sheltered and protected and to quell feeling of being lost or unloved or frightened at life's challenges.
Joining, for them, is more a sense of having a benevolent parent who is watching out for them, and having lots of brothers and sisters who care about them. They no longer feel like Houseman's "stranger, alone and afraid, in a world I never made." They have a family (in their psychology).
There is yet another motivation. This one relates to the responsibility of making choices. Both religion and statist political ideologies remove the most fundamental choices - making them for the person. The joiners put their souls in the hands of God. Or, trust their convictions to the party. This seems to leave them feeling empowered, so long as their direction and their actions are in accord with the fundamentals supplied by that bigger-than-themselves entity.
Sacrifice does go down easier for those who have forfeit the complete ownership of their lives, having given some key part over to God or State. To have done that already implies that it is of more value than you they are. And, as Joe has written, "If your religion says that your god has the answers, you can just assume that they know what they're talking about. If you sign up for some socialist endeavor, you can assume that the values of others are more reliable than your own." So, this giving of yourself to something-larger-than-you also leads to faith.
There is only one way in which it makes sense for an Objectivist, or someone of high self-esteem to feel like they are a part of something larger than themselves. That is the sense that because the world is knowable, and by being a competent and aware person, we can be left with a sense of living in a benevolent world. This makes that world feel like it is ours, more than it is a sense that we belong to it. It feels like we are home in the universe. This is kind of a self-esteem trick. When you are fully self-accepting, it automatically leaves you far more accepting of others which in turn makes them seem more benevolent. When you are fully responsible for yourself, you aren't hungering for someone to come pick up what you should be handling. When self-esteem feels high, there isn't a feeling that we need to be frightened in anticipation of what might come. Self-esteem is a partial antidote to totalitarianism, to calls for sacrifice, and to invitations to adopt things on faith. (Reason, critical thinking, and sound principles being the rest of that antidote).