I don't know that it's a "race-based policy", but I would say that the policy is definitely a race (and ethnicity) issue. The reason I distinguish is because "race-based" signifies intent to me where I'm not sure it's there. However, even if a policy is not intended to discriminate based on race or ethnicity, it can still be a race/ethnicity issue if it affects certain racial and ethnic groups more than it does others.
Ultimately, with a policy like the one described by the OP, not only would the lower class decrease in numbers more so than middle and upper classes, but blacks, Hispanics and Native Americans among others would decrease in numbers much more so than non-Hispanic whites. Because such a policy would affect certain groups more than others, that policy becomes an issue for those groups. In all fairness though, race and class would not be the only concerns. Those with mental illnesses, physical disabilities, lower education and so on would be affected as well making the policy an issue for several historically marginalized groups. It's just not a good idea.