Having worked at a theme park (for 2 months so far) the only people I've ever even considered looking twice at age-wise are people who are much much older than you (70/ 80 years old) and only out of admiration for their insatiable desire for adrenaline which I hope to have if I ever reach that age.
The majority (read 90+%) of the populace visiting (Thorpe Park) tend to be teens to middle aged people so there's still plenty of time for you to feel "old" when visiting a theme park.
That said, you become "too old" for theme parks when they stop being enjoyable days out and you're no longer excited by them in which case it's time for a new (and maybe even cheaper!) hobby .