I see so many here at RF adopting a range of beliefs from various religious systems and making up what appears to be their own personal religions.
How much of all this can be said about me, I'm not certain. Some of it probably. But I'll share my perspective, such as it is.
How authentic can such a blend of religions be, outside of that individual?
I'm not sure you can always call it a blend, which is syncretism, or just simply picking and choosing the best for something new, as organized religion didn't work for them. But to ask how authentic it is, that depends on the fruit that it bears in that person's life. "By their fruit you shall know them," said Jesus of Nazareth.
I've never understood that as "By their beliefs you shall know them". I see those as more just window dressing. You can find beliefs in any shop. But it's how you shine in them that matters. Not whether you bought them at the discount shop downtown, or from the Taj Mahal.
Does it matter if no one else shares that mix of beliefs?
As with anything, people seek communities, be that in some common interest area like classic train collectors, or the religious equivalent a vintage-class bible study group. Community gives strength and support to the individual, and common belief is what creates that community. Beliefs can be very mailable this way, biasing us towards group membership and away from things which threaten that. In other words, we can be pretty easily swayed with such a strong current in that river. Very few can truly go it alone.
So on some level yes. But if it means compromising too much, say one's intellect, one's sense of good reason and rationality, one's education, and such, then you may find those who prefer to be alone, than to sacrifice the gains outside formalized religion.
What is the motive behind syncretism, and is it merely “religion shopping” or selecting “ingredients” to fit personal religious tastes?
Excellent questions, by the way! I would say those who leave religion and become atheists do so because they find that rote answers from the 'Rote-Answers to Doubts' handbooks offer to most believers, to fall short for them. I'd be included in that number as well. But what makes some seek out other religious perspectives, outside the constraints of the previous religious system, is that they still believe in their hearts there is a "Divine" reality, even though the way it was talked about before failed to translate actual meaning into their lives.
People look for ways to understand God. But what some groups offer, fails to speak to them. So they look for other voices. And if their paths are true, they will find those who do speak Truth to them.
What role does God (or gods) play in the choices?
Central of course. They are after all seeking the Divine itself.
How many versions of religious truth can there be?
As many as there are humans. Each human being relates to God as themselves, not as other people. "God accept me because I'm in the right group", is a prayer guaranteed to fail.
How can one find the diamond in a pile of broken glass?
By realizing that diamonds are strewn throughout Creation, and people who are self-absorbed, see only their diamond as a diamond, and all the other diamonds as broken glass. No one human being has absolute truth restricted to their views. That is the opposite of Truth.