It has also been said that we don't need feminism dividing the workers' movement. Or we don't need the workers' movement dividing the national movement. We're all just people etc. (which is also true of course). But it seems it happens quite easily that, for all practical purposes, the more general term starts to refer only to the currently dominant group. So when discussing what "the people" need, it's really about what men need. Ditto for "national" interest, which might turn out to be the interests of the propertied and educated classes; "women's issues" = white heterosexual women's issues etc.

There is no idea someone will not take to a logical extreme and blow out of all proportion. I can't say whether or not this has happened to intersectionality to some extent, but if it feels that for some it's now a worldview and a confession of faith rather than an analytical tool, then to that extent it probably has happened. But that doesn't discredit the idea itself. Thatstealthygal's comment has it right IMO.

Also, an organisational split based on different political approaches might be principled and useful, or it might be a sectarian adventure. Which it is would have to estimated on a case by case basis, rather than on principles like unity or independence. Like intersectionality, organisational unity and organisational independence are tools, not principles, and there will always be disagreement on which tool is the right one in a given situation.