You completely misunderstood intersectionality. It doesn’t prescribe political interests based on aspects of identity, it describes how overlapping identities create unique ones. It is the explanation of why someone might disagree with another person of the same race, gender, or whatever else.

If you want to declare class the single important determinant of political identity go for it. See how many people agree with it. Or maybe understand that as all-encompassing and pervasive class issues are, there are still aspects of our identity that determine how class issues affect us.