defining when criticism of Israel becomes anti-Semitism
First things first, please do note that generalizations are that, generalizations. The point that I am going to disagree with the idea that attitudes towards anti-Semitism have changed does not mean that there cannot be cases of genuine anti-Semites in the Labour party (or in any other group of people big enough).
Vox has an interesting article on the issue.
On the basis on that:
Anti-Semitism has a - justified - very negative perception, making it useful for appeals to emotion. It is very useful to claim that your opponent is anti-Semite as an ad hominem which has a profound impact. Your opponent says four words, you have to carefully explain what your position is1.
The left is usually against the occupation of Palestine by Israeli forces and asks for an end of the military occupation of Palestine territories, mostly on the basis of a two state solution, based in borders similar to those of 1949, dismantling of colonies, shared Jerusalen, etc.
Regardless of its merits, it gives people2 a line of attack: "support of the Palestines or criticism of the Israel government is just disguised anti-Semitism"3. Even if the criticism comes from Jewish leftists, because "they do not know what true anti-Semitism is".
This also has put the same people in the left sharing arguments with true anti-Semite groups who just oppose anything Israel does. Which leads to guilt by association4 in some cases and in other cases to actual, serious mistakes.
And of course, when someone realy loses it (e.g. Ken Livingston and his refusal to apologize for his comments) it just becomes the "example" that justifies calling all/most of the Left anti-Semite. The fact that his comments have been answered by suspension from the Labour Party seems not to be taken into consideration.
Regarding the UK, the issue seems to have become more relevant since Jeremy Corbyn was elected leader of the Labour Party. Mr. Corbyn has been more left-leaning than a significant part of his party, and has been openly criticized by a section of it5.
He does have some well deserved polemics:
So far the more damning would be a report that he called representatives from Hamas and Hizbulla "friends". He publicly regretted that, but I think it is still a grave mistake.
Another one would be the mural that is alluded by the OP, and that he claims he was defending -without having noticed its anti-Semitic content- on the grounds of freedom of speech.
Things that do have changed:
Jeremy Corbyn is the leader of the Labour Party. And, regardless if you agree with it or not, criticism of him is always going to have a bigger impact that the same criticism if he were just a base member of the Party, or even a MP. It goes with the position.
Social media. It is not new. But the first line politicians that appear today did use social media before being first line politicians. Even if Gordon Brown or David Cameron did get to use, say, Twitter, they would have used it while being conscient of his public position and would have avoided inflamatory statements. But first line politicians of today probably did use social media before getting their positions. That makes it easier to analyze everything they have posted in search of anything that could be polemic.
Consider how easy would be to call somebody supporting the Dalai Lama "anti-Sinicist". Yet it does not have the same strength, doesn't it?
2 Either because they support Israel government position, or because it is a way of attacking the left, or because the sincerely believe it is anti-Semitism.
3 Recently there was a manifestation in Paris against a recent anti-semitic crime. Of which Jean Luc Melenchon was expelled just because he supports a boycott of Israel due to the occupation of Palestine. Again, generalizations are unfair and there have been criticism of this by Jewish people, including the son of the woman who was murdered.
Do you imagine being prevented from condemning the murder of a Russian citizen because you support economic sanctions against Russian intervention in Ukraine?
UPDATE: Link in English to the news related in the above link. It has been harder to find that I thought, because most English online newspapers seem to have given more attention to the expulsion of Marine Le Pen; explaining Melenchon just for "claims of anti-Semites in his party". As a result, I do not know if the source is reliable, but it seems to be from Israel.
4 And in case you want to argue that guilt by association is guilt, let's remember USA's BFF in the Middle East. Or this other friend of dictators
5 Of course, criticism of a leader from his own party is always more newsworthy than criticism from other sources. Regardless of the basis or motive of the criticism, it shows that there is internal conflict in the party.