I really question this. Most Disney movies targeted children and families. Family entertainment is not very political. Most people were not hippies or radical leftists. Disney films might be mocked by the new cultural elites and art critics in the same way they mocked Norman Rockwell's art, but Rockwell was always very popular. Most people left of the center still held those "conservative" values. The Wonderful World of Walt Disney TV anthology show was still being shown all throughout this time. Its ratings decline were because the quality of shows had declined. In fact, as the times get worse in the late sixties and seventies, escapism through Disney films might make these new movies and shows even more popular.
If Walt Disney could still impart the same creative vitality and quality to his animated films and TV shows that he had earlier, I think they'll be just as popular as ever.
Plus we have to remember that a conservative in the mid to late 60's is not necessary the same as a conservative now. Supposedly there is a rumor that Walt was wearing a Goldwater button when he got the Medal of Freedom from Johnson. Now let's look at Goldwater's policies and put them through a current political spectrum test. Chances are, Goldwater would rank as a libertarian today rather than a conservative. I strongly feel that Walt would be the same. If he was alive today, he probably would not have like Obama, but I really doubt he'd be supporting Trump.