Yes, certainly when it comes to science there is nothing in it which rules out religious belief, as evidenced by the large numbers of scientifically literate people who follow a religion.
There are almost as many varieties of religion as there are people, so obviously there's a huge range of things that different people believe.
Scientology is a religion, even though it's plainly ludicrous - so much so that its leadership keeps all the most insane bits hidden far away from new
customers clients marks followers.
Scientifically literate religious people tend to cherry pick the parts of mainstream religions that mesh best with their own moral compasses, while ignoring the more unsavory bits and pieces, and the bits that are directly contradicted by science. People are very good at compartmentalising. And if you want to think of yourself as religious but you aren't impressed by the mainstream dogmas, you can always be a deist or adopt some kind of watered-down version of one of the mainstream faiths. Failing that, you can make up your own god to suit yourself.
You're right that science can't "rule out religious belief". It can't even rule out the possibility that one or more gods are real. It can, however, place rather strict limits on what those gods are capable of doing in the world, because the world looks essentially indistinguishable from how we'd expect it to look if there were no gods at all, as far as our science can tell.
A lot of the earlier Dawkins polemic was simply knocking down creationism...
He was doing that long before he went public with
The God Delusion.
... which is not part of mainstream Christianity (nor Judaism either, I rather think)...
Only because mainstream Christians, for the most part, have stopped insisting that every verse in the bible must be literally true, at least insofar as it talks about facts about the material world that are checkable.
We can argue the extent to which American evangelical Christianities are "mainstream", of course. Seems to me like they are mainstream in the United States, given the percentages of self-declared American Christians who identify that way.
The focus on creationist ideas about life (i.e. biology, Dawkins' own field) is why I wonder if the New Atheism initiative may have been in part a reaction to the Intelligent Design movement in the US (1995-2005 ish) which at one stage looked rather frighteningly as if it would get mainstream political endorsement and become hard to dislodge.
There was no "New Atheism" initiative, as such. Coincidentally, four best-selling books were written withing several years of one another. At the relevant time, the world was also dealing with the evils of Al Qaeda and the Taliban and the fallout from 9/11. It meant that a lot of people were receptive to arguments against religious extremism of all stripes. Once you're tackling religious extremism, the logical next step is to question the foundations of such.
The battle against Creationism and, later, the Intelligent Design trojan horse, had been going on for a century before 9/11.
As explaining the natural world is not the purpose of religion, which is basically to provide guidance to help people live their lives...
That's a relatively modern view. Following the Enlightenment and the scientific successes of the industrial revolution and beyond, people realised that the mainstream religious texts do a very bad job of predicting or explaining the natural world. So, the popular view these days is that it's okay to pretend that the bible doesn't say things like pi=3, or ignore it when it does. The bible is still held by many to be morally authoritative, though. And
that requires that one similarly ignores the many odious immoral examples that the bible documents, both from God himself and from his most valued followers and prophets. The usual excuse is that "people had different morals back in ancient times, and they were appropriate back then, when the bible was written". So, free pass to slavery and giving your wife up to a rapist gang, and so on, as long as it happened in "biblical times" (although, having said that, people were still making arguments for racism based on the authority of the bible back in the time of the US Civil War era, and there are still people
today who apologise for slavery by waving biblical verses).