In the British system, the Monarch can only intervene in very specific circumstances. They don't apply in the cases being talked about here. Parliament had the legal right to pass abortion laws - it's not a constitutional issue and the Queen could not withhold the Royal Assent. And the idea that Muslims have taken over Britain is abject nonsense. There are enclaves in the UK where Muslims are a majority, and they have more influence than I'd like, but they are not even close to having taken over.
But what is the overall trend in regards to Britain? I understand that in most cases the monarch should not - or cannot - intervene, but then what is the purpose of the monarchy? As a token national symbol? As a check on a nonexistent parliamentary tyrant?
Oh, and I do freely admit that I am anti-monarchist. So my views in that regard are not always the most rational.