Donald Trump has suspended the entire US refugee programme and restricted travel from certain Muslim-majority countries. In some ways the order he signed was chaotically unclear, leading to vast confusion at airports and consulates as to who was allowed in and who wasn't. It's working out very nicely, he said.

In other ways it was very clear indeed. Whatever the rest of the world thinks – and most of the world thought the US policy was working pretty well – he was going to make it much, much harder for Muslims. Trump is not saying exactly that if they are not choirboys, they must be terrorists. But Muslims are certainly going to have to work much harder to convince the authorities of their innocence.

And most of the world really doesn't like it. They don't buy the national security argument; they think Trump is stoking fear and hatred for reasons of his own. There have been demonstrations and protests across the globe. Otherwise non-political people have taken to the streets in surprising numbers.

Last night I was one of them, as much for research purposes as anything else. I live in a small town in the English Cotswolds. It's an elegant sort of place with lots of Regency buildings, a minor university, lots of posh shops and a couple of theatres. It has a Tory MP and the one before him was Liberal Democrat; he was evidently organising the protest, which was on the tree-lined promenade and attracted around 300 people. It takes a lot to get people to demonstrate in Cheltenham, especially in the rain. And it was a very genteel protest; cheerful families, the odd chant and even odder signs: "Donald Trump is not a very nice man", "I remember when the annoying Orange was just a YouTube channel", and – my personal favourite – "I'm really quite cross". The speakers talked politely and semi-audibly when they really ought to have shouted. It was all very English.

That doesn't mean they didn't feel deeply about the issues.

I asked a few people why they were there and what they thought about Trump. One young mother said she found him frightening, instancing his attitude to women and Muslims. Another said she didn't want her children growing up with him as a role model. Another said she was part of a mixed-race family and believed Trump's America would be one of segregation and intercommunal strife.

What was interesting was the depth of their rejection of Trump and all his works. There have been demonstrations before, even in Cheltenham. There was plenty of opposition to the Iraq war, and some hard things said about George W Bush as well as Tony Blair. But I haven't seen this level of fear and worry before. This wasn't politics, it was morality – not just personal, sexual morality of the kind highlighted by some Christian anti-Trump campaigners during the election campaigners, but morality as ethics: they believed he was fundamentally, dangerously wrong about basic values.

Of course, Americans might ask what it's got to do with us anyway, and it's a fair question. One answer is that Cheltenham is the home is the home of GCHQ, where the government does its spying from, and lots of Americans work there. Americans were even represented at the demo. But another is that this is a world affair, not just a US one, just because of America's position in the world.

I don't know how Trump's presidency will develop. Last Sunday we interceded for him in church, sincerely and sombrely. We prayed God would give him wisdom, just as we've always prayed for world leaders. But there was an undertone of unease even in those prayers. The world felt dangerous, and we weren't just praying about competence, but about character.

There are plenty of Trump supporters who think this is nonsense. Most Americans, judging by the popular vote, don't. In much of the rest of the world, there are the same doubts, not just about his head, but about his heart; the kind I heard expressed in my small spa town last night.

We'll carry on praying. Trump needs it; so does America, and so does the world.

Follow Mark Woods on Twitter: @RevMarkWoods