Do my parents have to claim me as a tax dependent for me to be on their health plan to age 26?

Individuals with coverage | Issues For Young Adults: Student Health Plans and Coverage on Parent’s Health Plans

No. You do not need to be a tax dependent of your parents to continue to be covered as a dependent on their health plan. (45 C.F.R. § 147.120).

Individuals with no coverage
Individuals with coverage
Coverage for small employers
Post enrollment issues