This is really all very old news. Don't mistake the attitudes of individuals for those of organisations. If an individual team chooses not to dance with another, that is up to its members; the Ring is just an umbrella organisation and has, so far as I know, no rules concerning that. It merely restricts its membership to all-male teams. Who does or doesn't get invited to dinner afterwards is presumably a decision made by the individuals organising the event.

Morris isn't my subject, though inevitably I know a lot of people of both sexes who are involved in it. Dick may find the following helpful in forming an opinion based on what is going on today rather than a quarter of a century ago:

The Morris Ring was founded in 1934, the original member teams being all from the Revival. The Women's Morris Federation was founded in 1975. In 1980 it decided to admit mixed as well as women-only teams, and in 1982 became open to all. 'Women's' was dropped from the name in 1983. Meanwhile (1979), a third organisation, Open Morris, was founded to counter the single-sex policies of the other two.

All three organisations continue in, so far as I know, perfectly good health; and on perfectly good speaking terms with each other. As (again, so far as I know) the only national organisation until 1975, the Ring naturally lost members to Open Morris and, later, the Federation; but over the last 20 years everything seems to have settled down and I doubt if there is a lot of movement of membership between the three.

Given that ceremonial dance teams (whatever they dance) typically have a quite short lifespan and I would guess (though others will have to confirm or deny that guess) that the majority of teams currently dancing were founded less than 20 years ago in any case, then if they have joined any of the umbrella organisations, they will probably have gone directly to whichever one best suited them (or may indeed be attached to more than one).

http://www.themorrisring.org/

http://www.morrisfed.org/

http://www.open-morris.com/