I haven't watched many of the Disney movies, because of that reason, Humby. The only Disney movies that I've watched are some of the older ones, like Mary Poppins, as well as some of the princess ones, like "Cinderella," "Beauty and the Beast," "Snow White," and "Tangled" (Rapunzel). My parents never let me watch "The Little Mermaid" because she disobeyed her father, and they made it look okay. Now that I'm old enough that I could watch it, I don't frankly care about doing so.
Any Disney movies I've watched are borrowed from the library or elsewhere, because my family doesn't support Disney in any way.
You do want to keep in mind how this will affect your children in the current culture.
I am glad that my parents didn't let me watch all the Disney movies that I wanted to. However, I appreciate that they let me watch some of the most classic ones, so that I don't feel misplaced in our culture. After every (rare) time that I watched a Disney movie with my siblings, my parents would talk with us about what isn't right in it. For example: in "Snow White," the witchcraft wasn't right, it wasn't right that the Prince kissed her before they were married, and, as with all Disney princess movies, they made the princess (Snow White) seem very beautiful by the world's standards, and perfect all the way around. Because of that last reason, we weren't allowed to watch any Disney princess movie whenever we wanted, but we were familiar with the basic story lines.
Because my parents did it this way for some of the most classic Disney movies, I not only am able to better relate with our current culture (which comes in handy when witnessing to others about Jesus), but it also helped me develop my critical thinking at an early age. Instead of my parents completely
protecting me from any and all bad, they showed me how to think through the rights and wrongs of of movies and books.