Thanksgiving is on my son's birthday.
As an aside, I have to recommend you consider celebrating your son's birthday at the Disney Thanksgiving Day Family Feast in the
Disneyland Hotel Grand Ballroom. It's a beautiful annual tradition at Disneyland filled with a vast buffet of foods, live music (dancing encouraged!), character meet and greets, and festive fall decorations that fills the entire hotel ballroom on Thanksgiving Day with seatings from 12 p.m. to 6 p.m. It's on the pricier side and they moved to prepayment required last year, but it's worth it enough to us that our family makes it a point to do this every year. ADRs typically open up (usually to long phone queues and technical difficulties on the website) in September, 60 days prior to Thanksgiving, and reservations fill up within a day or two (don't wait).
Since our family tends to go every year for Thanksgiving week, I'd say generally the crowds are manageable. Thanksgiving Day tends to be the lightest day, the Friday morning after is light but crowds build progressively throughout the day, and Saturday and Sunday tend to be the heaviest days during that weekend.
As an indicator of crowds, I would check the AP blockout calendar. For the week of Thanksgiving, SoCal Select and SoCal APs are good to go on Monday, Tuesday, and Wednesday, then blocked out on Thursday, Friday, and Saturday; the SoCal pass is open again on Sunday, but the SoCal Select remains blocked. The Deluxe AP is good to go on Monday, Tuesday, Wednesday, and Thursday, but blocked out for Friday and Saturday after Thanksgiving, and open again on Sunday. So you can probably expect the Monday, Tuesday, and Wednesday leading up to Thanksgiving to be crazy when the locals come to get their Disney fix before the holiday weekend, and again on Sunday to make the most of the weekend. I'd add that this week should be peak pricing for single day tickets, so that could help deter some crowds.