I would just add that Violet Alford's theories, referred to above, were already out of date when she published them and are not taken very seriously by more recent researchers. It is unsafe to draw conclusions from them, particularly in relation to potentially sensitive issues, and I wouldn't be too quick to dismiss the "disguise" aspect, particularly as that wasn't a guess made by folklorists, but the result of asking performers why they did it.

It is also the case that the American experience is very different from the British, and you do need to be careful when drawing analogies between them: many, while they may look fine on paper, will turn out to be misleading (or entirely specious) in practice. A little learning is a dangerous thing. For example, there seems to be an assumption made by a number of contributors to this discussion that Mumming (the British, not American, form) and Morris are the same thing; they are not, though the customs have often overlapped; and that all mummers black their faces. That too is not the case. Some do, some don't, depending on their particular tradition.

No one, I think, is suggesting that traditions should not be "allowed to evolve". It is another matter, however, when traditions are bowdlerised or otherwise mutilated at the behest of outsiders who do not understand them or their context, and may indeed never actually have seen them or met the people of whose lives they are a part. Understanding must always be the first step in matters of this kind, and the onus of justification, and proof, must be on the person who seeks to suppress or to impose change. We have more than one anonymous "guest" here, perhaps; at any rate, innuendo and false analogy do not make convincing arguments, even when repeated.

A very useful resource to consult when looking at aspects of the mummers' play and other traditional drama is Folk Play Research: Traditional Drama Research Group. You will find a lot of material there, and suggestions for further reading which will give a more accurate and balanced impression than is likely to be got from writers like Alford. On the separate (but related) subject of Morris, see also the bibliographies at The English Folk Dance and Song Society.