I think (this is an unresearched assumption) that the Islamophilia on the left results from the stance of championing the underdog / victim of oppression. You see this ethos in the statements of the BDS celebrities like Roger Waters.

But as I take you to suggest, the American (and perhaps other) Islamophilia tends to ignore those populations who are oppressed by militant Islamists or wealthy wahhabi (Kurds, women, Christians). It's simplistic binarism, which is typical of most American (and apparently British / European) thinking. Although the popular right wing / Christian evangelistic frame of mind tends to be Islamophobic, politicians on the right typically ignore the victims of Islamist repression, as we saw with the Kashoggi murder or Trump's sacrifice of the Kurds to help his allies in Syria / Turkey / Russia. These opportunistic politicos know on which side of the bread the butter is.

I'm not a political theorist / historian, but it seems to me that the situation is not a zero sum game. You won't decrease oppression of all Palestinians by increasing oppression of all Israelis (e.g. via BDS). There has to be a win-win solution, but the winning will require sacrifice and forethought, and not just from Palestinians and Israelis.