"In the UK we are rarely concerned with or even aware of the religious beliefs of our politicians..."

I have heard that in several European countries this is the case. Here, it is about the first thing that is ferreted out by opponents.
When Dwight Eisenhower was nominated in 1952, he had to go very quickly and FIND a nice, easy-to-tolerate church to attend, and then to be seen there. As far as I know, that is as close as we ever came to a 'non-religious' president.

.... Bill had set of missionaries going out ...

That was only the most obvious example. In some places in this country, (mostly Southern and MidWestern)(I lived in Wichita, where that abortion doctor was murdered) it is difficult to even live peacefully if you admit or advertise that you do NOT go to church. This is not a joke....and in those areas, do not even consider running for any major office if you are not known to be Christian. You will simply be branded as heathen and 'connected' to every sin known.

Jon... I find it hard to comprehend that there is anyone who has NOT "heard the word". What happens...whether YOU would limit it or not.... is that "hearing" is coupled with peer pressure and fear and distortion of history-- and often supported by illegal, but tolerated, teaching in the schools. When I was in 7th grade, my science teacher organized the Christmas pagent, and my class was TOLD we were to participate and memorize the lines about shepherds and angels and Bethlehem. At that time, I was a good Methodist but, and never even wondered if anyone in my class was uncomfortable with it all. All I know is, it was inserted into our lives as if there were NO doubt. Well, that was 1952, and there are 'some' more rules now....but in many areas, breaking or ignoring those rules is the regular practice, since the majority would make life miserably for those who tried to opt out.
*sigh*...it is sad to remember all this and to have to make these hard points, but it IS the case that "freedom" does mean 'freedom FROM religion' as well as 'freedom TO engage in religion'.