I would say that the UU are not religious but some of them are very spiritual.
One person that I can think of who is not religious but is the most spiritual person I know - Carolyn McDade.
Many, perhaps most, of us UUs are both. We would not be part of a religious organization if we did not value religion in some way.
I think that the problem is that there are many flavours of SBNR.
For some, it's just something they toss around to explain why they are not in church. They are really not particularly spiritual but feel they can't just say "I don't go to church because it's boring" or "because I think it's useless". If you honestly do not want to be in church, then say that. Don't use the SBNR line unless you really are interested in spiritual matters.
Then there are the seekers who find traditional religious institutions too restrictive but still pursue spiritual quests in various ways, whether that's reading, listening to Tapestry, viewing Great Courses videos, getting out into Nature, or whatever. I was there for a while myself. Some will always be this way, some will eventually land back into some kind of organized faith.
And there are those who simply do not see the need for formal religion but who still feel a deep connection to Existence. They may live that connection through good works, sharing and caring, and so on.
IOW, don't tar the SBNR with one brush any more than you would tar Christians, UUs, atheists, or any other group with one brush. There are variations and shades of understanding.