People clump. They clump into groups that like baseball players who wear one color of hat so that they can hate baseball players who wear another color of hat. They clump to go watch birds together. They clump to quietly read books together. Young people clump depending on whether their interests lie in football, the arts, academics, or defiance. People even clump to share their nonbelief with each other.
People will clump around spirituality as long as there are people and they have common opinions concerning spirituality. We call those clumps "religion". And as long as some clumps of humans are inclined to get aggressive towards other clumps of humans or humans who remain unclumped, we'll have problems with clumps, including religions, behaving badly.
Religion is certainly not a requirement of spirituality. Nor is spirituality a requirement of religion: Unitarianism in particular contains open atheists, and, on a much less conscious level, a great many people who belong to religions have very little grasp of what their religion's spiritual views actually are.
I take a perverse delight in informing, say, "devout" -- meaning militantly for their team and against the rival teams, and not meaning spiritually active-- Roman Catholics of the Church's social teachings ("go-team-go!" attitudes are strongly correlated with what is called the authoritarian follower personality by sociologists, and authoritarian followers almost always hate the disadvantaged).
Let me emphasize again here that I'm using Catholicism as an example: this sort of person, who is more aware of which team he or she is on than what that team stands for, can be found in every religion. This is because religions are, largely, social clubs, so much so that some of their members are there almost entirely for the social activity.
This also works in the opposite direction btw : there are religions whose founders embraced ideas most modern people find offensive, but many sects have explained them away and many members are entirely unaware of them-- for example, the Buddha's teachings on women. Modern people rarely countenance gross gender inequality, and so Buddhists make those embarrassing teachings disappear.
All this said, my eyes wide open, I'm a big supporter of religion. Private spiritual practice doesn't require the presence of others. But having a shoulder to lean on, having an ear that will listen, knowing who in your community needs your condolences, having somewhere to gather for dinners and parties and bingo games and the people to gather with, having someone to approach for advice, having a base to organize doing good things great and small, or even as the core of a great national movement for justice --- for all this and more, you need religion and other forms of social organization.