It is strange that the people annoyed most by the tendency of individuals to call themselves spiritual but not religious are not religious believers, but atheists.
It is primarily caused by the fact that people love the central philosophy of most religions, since it is all about being nice to people and a theoretical world where they are nice back. But they are put off by the priests, imams and gurus who keep making rules, not from a feeling of love, but from their own egos.
So you would think that it would be religious authorities who would get angry about people saying they are not religious, but still feel connected to the heavenly realm. But they don't, possibly because they are too busy telling their remaining flock what to do/ not to do.
Instead, it is atheists who make a fuss about it. When all beliefs about a reality beyond what we can know with out worldly senses came from religion, it was easy to laugh off - religion was a form of control, a way of making money, the powerful manipulating the weak. It was the Tyrant's tool for making his subjects submissive; "I may be fucking you over today, but don't worry, you'll be rewarded in heaven". But now, today, the masses are (in general) not being manipulated by anyone (so directly), yet they still choose to believe the same kind of things as before. Proving the 19th Century atheist dogma was (at least partially) wrong.
But of course, spirituality was around long before religion. Human beings are naturally spiritually inclined: it is unnatural to deny what cannot be disproved, just because it cannot be proved either. Rejecting religion but upholding Spirituality is about telling both the bearded priest and the bearded professor that neither of them have a monopoly on human understanding, and neither have a right to tell you what you believe.
Another trend is for the separation of religion from spirituality without abandoning either. People may insist they are pious, practicing members of their religion, whilst at the same time refusing to accept the mainstream dogma. I would put myself in this category, I’m a Muslim, and but I also do the Latihan of Subud, which I do not believe is incompatible with Islam, but Imams tend to think otherwise.
So it is a perfectly natural, when people are given the freedom to categorise themselves, not to accept the labels formerly stamped upon them. If only we could win the tolerance of those who do not want to believe at all…