First stating the obvious -- Disney is busy. All the time. (Though last year @ DL Paris was pleasantly light crowds).
That said -- we always do Disney at Thanksgiving, always
Disneyland California except for last year when we did Paris. Our "usual" days are the Friday AFTER Thanksgiving through Tuesday (kids miss 2 days of school).
A few years ago, we decided to try the days BEFORE Thanksgiving, so the kids would miss no school. We are always in Dallas ON Thanksgiving for a football game and dinner, so never at Disney ON Thanksgiving.
One try during the days before Thanksgiving was enough to convince us that we are much better off AFTER. The OVERALL experience, for us, was MUCH MORE CROWDED in the lead-up to Thanksgiving compared to the wind down after.
For us, though, that MONDAY after Thanksgiving is a game-changer. That is basically an offseason, weekday, non-holiday day. In other words, about as light as you'll ever find Disneyland. If we couldn't have the full day on Monday (Tuesday is our travel day), it might change our feeling. Friday is crazy busy, Saturday basically the same or worse. Sunday starts to lighten, especially a bit later in the day, and Monday is great!
But, then again, every day at Disneyland is great to us!
Good luck with whatever you do!