I understand what you're saying and I largely agree with the sentiment.
I think, however, political left is the wrong term when what is being referred to is the fringes and not the mainstay.
The group you talk about in your second paragraph I would call the extreme or ultra left, just as I would call Farage and his bunch extreme right and the likes of Netanyahu ultra zionist.
Political left sounds like you are talking about the people in the Labour party, SNP, Greens, Lib Dems - and we should acknowledge that the current politically left government have designated Free Palestine as a terrorist organisation and continued to send arms to Israel - so to say that they support anti-semitism wreaks of cognitive dissonance.
The grooming gangs in Rochdale were horrendous and the lack of action for fear of being seen as racist cost many young women and girls dearly.
However, I know people who work in the public services up there and it didn't come from being enthralled with muslims or seeing them as victims, it came from a genuine desire to not be prejudice. It was obviously the wrong way to have gone about things and they have learned a lot and are making positive changes that are good for both communities as a result.
I don't believe they had the same motivation that the extreme left have, which in reality, has absolutely nothing to do with seeing Muslims as victims and everything to do with being antisemitic. For those people, Muslims are a useful front and the marches are something to hijack in order to harras and intimidate and it should absolutely be called out.
So if marches were stopped, how can people who want to protest the needless death and destruction in Gaza and ongoing land grabs in the West Bank and our governments role in it, how can they do that in a way that won't get hijacked by the extreme left and get them labelled as antisemitic?
Because, as you rightly point out, tacit support and silence can be just as damaging.