The literature on this topic is confusing. Some places say that a non parametric bootstrap still needs the constant variance assumption.
Are they talking about the coefficient estimates themselves? Because I don’t see why it is needed if you bootstrap the F or t statistic distribution under an artificial null hypothesis created by resampling and permuting the data with replacement.
Can’t you just compare your observed t/F stat to this resampled null distribution? Does this factor into account heteroscedasticity already?