Classical Marxist/Lenninism is specifically not intersectional. They'll use race as a lever against capitalism but deny race as a social problem they must specifically intervene on. But it's also stupid to adopt. There's a reason TERFs are often fascist adjacent.
I think it's like saying that Marxism isn't... let's say, Nietzschean. Those are two ways of looking into problems. In some points, they'll coincide; in others, they won't. I'm bad at analogies. Anyway, if you're a Nietzschean (in this case, if you believe intersectionality is the proper way of looking at social phenomena), of course Marxism (probably in all its different branches) will look incomplete and like they're building from the wrong premises to you. But if you were Marxist, you'd think the same of Nietzschean philosophy (or intersectionality).
I'm sure both have excellent reasons to believe in a framework or another, but we should not forget they are just that, not truth™. I say this not to fall into an absolute relativism but to prevent any side from falling into a conviction of moral superiority. We cannot be so sure about it.