Whilst minstrely may have had some influence I suspect a less racist source for blacking up.
In days gone by begging was frowned upon socialy.
Morris has been used as a way of making money for drink and in the days before welfare as a way of raising money to feed families during
times when work was short for any reason.
Dancers would have disguised themselves to hide the shame of begging from their neighbours.
In Cornwall at certain times of year "geeze dancers" appeared so called because they wore disguise when dancing.