I remember about 15 or 20 years ago when Alpha was new, they were advertising in newspapers and on buses. It seemed weirdly un-British and didn't last long. (The course is still going, I just only see the branding on actual churches now)

That's because churches in the UK are all bankrupt, more or less. I vaguely recall seeing ads for churches or Christianity in general in the UK some time ago, and I still see pro-Christian ads (usually just bible quotes) in Switzerland.

There are mega churches in the US which push the prosperity theology https://en.wikipedia.org/wiki/Prosperity_theology Many of their pastors make several million USD every year.

Also, There is a strong overlap between conservatives and right leaning politicians.

So there are money and power motives

Majority of the religious ads I see are for church services or special events. What time, where, etc. There are many aimed at proselytization. There's a surprising number which are just sermons in text form, or just rants. Plus there's people flogging their book, podcast or Youtube channel. And then there's a fair amount of religious tchotchke. T-shirts, crosses as jewelry, custom Bibles, etc.

The rants I find most interesting. They almost never want to sell anything. They just really wanted you to read what they had written and paid for the privilege.

It seems somewhat shady, there is a profit motive?

Maybe it is about conversion, which at least has honorable intentions.

When I drove through the US South, I saw all sorts of anti-abortion church billboards, so maybe this?

>I live in the UK and have literally never seen an ad from a church

To be honest, the UK hardly has a church anyway :-)

money? their income is donations from the flock