Could it be beneficial for me to not disclose my gender/ethnicity in an REU application?
I am an undergraduate in the US applying to REUs in mathematics. [...] I am a white male from a suburban area. Clearly this is not going to boost my application


The personal consequences for you of being labeled on your application as a white male are not something that anyone can predict with any certainty. Even assuming that the data are visible to the people evaluating your application (which is probably not the case), the putative effect would depend on things like the individual attitudes of people evaluating your application. These attitudes would be variable and we have no way of measuring them.

Keep in mind that any pile of applications in mathematics in the US is going to contain vast numbers of white males, so even if there were some very strong bias against you, or some extremely aggressive affirmative action program, the result can't possibly be to exclude all white males.

Since the actual consequences of your disclosing your information or not disclosing it are unknowable and probably negligible on an individual level, your guess about those consequences is not a good criterion on which to base your choice.

You might instead want to base this on your political opinions. Reasonable people can be for or against the idea of having the US federal government classify people into racial categories. An example of a reason for: a horrific national history of slavery and oppression, which we could try to undo to some extent. An example of a reason against: race is a nonsensical and artificial construct, and there is no logical way to apply it to people of mixed race.

If your personal utopia is one that lies on one side or the other of this issue, be the change that you want to make.