This article puts a lot of quotes around "identity politics", and "intersectionality" as a related perspective. As we may recall, the term "identity politics" itself was rejected for being unclear by the Libcom crew (see my debate last year on this thread). Likewise, the ISO's liquidation now is accompanied by a text (3 April on socialistworker.org) offering a critical defense of "identity politics", based on the same reasoning:
Socialists can start by rejecting over-simplified criticisms of what is called “identity politics.” In fact, we should probably stop using the term altogether because its meaning is unclear and imprecise — and gets in the way of connecting with people from marginalized and oppressed communities.
A by now common argument against identity politics is that it fosters a logic that allows for the rise of white identity politics (also mentioned in a footnote of the above article). This is, I would say, the main motive of critics of identity politics, whether they are Marxists or even rightwingers like Jonah Goldberg (taking an anti-tribal/collectivist position; or also reflected in the slogan: we have personalities, we are not identities). This argument is, naturally, dismissed by the idpol-defenders as an apology for fascism, enabling white supremacy (or being itself strasserist).
As to the anti-semitism dispute, the article mentions that Zionism was a kind of identity politics, traces of which indeed are reflected as far back as in the Bund (criticised by Lenin and young Stalin), which is incidentally noted by Jenny Bourne's 1987 article on Jewish feminist identity politics (as I linked on Libcom). By the way, we must not only criticise "bourgeois" identity politics, but also and especially its socialist/workers variation.
The article does not venture deep into the question of criticism of Israel/Zionism etc. It just notes that from the standpoint of idpol-defenders, the critics of Zionism could equally be seen as motivated by Jew-hatred or national chauvinism (the emphasized distinction between Jews and Jews-as-Zionists/Jewish-state has little weight; if the right to self-determination is recognised in principle for everyone else, but denied to the Jews, then this is also discrimination).
Or for instance, take criticism of Jewish religion, and practices like circumcision, which is not necessarily anti-semitic either; it is perfectly "legitimate" from an enlightened universalist standpoint to criticse it. But if someone's focus is mostly on attacking the Jewish religion, cultural traditions and even (alleged) cultural habits, then this criticism will be regarded as suspicious, as perhaps motivated by prejudice. It can be interpreted as an attack on Jewish "identity", although strictly speaking it is not racist, not an attack on Jews as a mere ethnic/"racial" group. Thus Lenin's criticism of the Bund was an attack on its "identity politics", and in fact Lenin (and the Marxists in general like Kautsky) would today be criticized for not paying sufficient attention to anti-semitism, and thus being complicit in it. Just like Lenin and the Bolsheviks are attacked for not being in favour of "sex-work".