How much do you think the average Palestinian cares about the welfare of the average Brit, or Canadian, or Belgian, or anyone else?
I don't know any, but I'm going to guess the answer is not very much, or more likely not at all. Most people simply don't, I don't expect them to or criticise them for it, it would be absolutely normal and completely understandable.
We're not the head of an empire or a superpower, we can't solve the world's problems, we're just a little island off Europe's coast. We need to keep out of anything that doesn't involve us, we have plenty of our own problems to deal with.
Pro-Palestinian protests are often hiding another agenda. Most likely anti-semitism. Pro-Isreali protests are likely to be anti-islamic in nature. The two sides are never going to agree, neither is all right and neither is all wrong. If you're taking a side then you're adding to the sheer stupidity of it all.