Being an atheist is expressly OK in the UK Scout movement (in fact, I'd say it's probably true of a decent majority of our adult and young members), and there's nothing in the scout values that people promise to uphold which require religion in any sense.
The duty to the Queen bit is a little bit more tricky. I'm a republican (and a scout leader) and concluded I was happy to follow the wording. The reason being that it doesn't define the scope of the duty, especially not in terms I would find problematic. The traditional scope of the duty is to keep the peace and not commit treason, both of which are required by statute law in any case. I don't see it as incompatible with wanting a change in the country's constitutional arrangements. And certainly the Scout movement wouldn't insist otherwise.
The duty to the Queen bit is a little bit more tricky. I'm a republican (and a scout leader) and concluded I was happy to follow the wording. The reason being that it doesn't define the scope of the duty, especially not in terms I would find problematic. The traditional scope of the duty is to keep the peace and not commit treason, both of which are required by statute law in any case. I don't see it as incompatible with wanting a change in the country's constitutional arrangements. And certainly the Scout movement wouldn't insist otherwise.