Is Kilimanjaro realistic for someone in their 60s who is pretty fit and active?

The main routes up Kilimanjaro involve no technical climbing and really involve nothing more than a long slog. There’s no reason why an older person (or young though, 10 is the legal minimum) of decent fitness cannot climb Kilimanjaro. The big thing to remember is that because of cost most trips are shorter than they really should be and many people get altitude sickness. It’s worth factoring in an extra day or so to allow for proper acclimatisation.