With the decline of religious observance, no secular alternative to these organizations has arisen, and this may be part of the "crisis of civic life" that some (like Harvard Professor Robert Putnam) think is occurring in many parts of the western world. People are segregating themselves on the basis of money, class more forcefully than before, and there are few safe spaces in which they can come together and appreciate each other, discussing important questions about what it means to live together with others.
I've seen (as a teacher) the effect of communities that do not have a shared identity or a common space in which to discuss existential questions. There is an almost palpable lack of "connectedness", of moral sensibility, of feelings of responsibility for others. I've also seen the powerful effect of bringing people together in a non-religious context to share an experience, most notably as a prison educator. Indeed, I've seen the value of the religious institutions "from the inside" (as a choirboy for many years). But I believe that not only do such institutions not have to be religious, but they may be even more effective if they are not, since you then eradicate the final barrier - that between people of different faiths.
In short, humanism / secularism / atheism is often presented as a negative position. We're "against" god, "against" irrationalism etc. And we often spend much of our time debunking things - religious arguments, homeopathy, pseudoscience, cults etc. Instead, we absolutely must spend more time building positive institutions to achieve social change. If we really believe that a society in which reason, rational method, clear thinking, and respect for all human beings would be a better society, we have to go out and build it. Debunking is not enough.