According to the International Society for Mountain Medicine, in its article Normal Acclimitization:
Acclimatization is the process of the body adjusting to the decreased
availability of oxygen at high altitudes. It is a slow process, taking
place over a period of days to weeks. High altitude is defined as:
•High Altitude: 1500 - 3500 m (5000 - 11500 ft)
•Very High Altitude: 3500 - 5500 m (11500 - 18000 ft)
•Extreme Altitude: above 5500 m
Practically speaking, however, we generally don't worry much about
elevations below about 2500 m (8000 ft) since altitude illness rarely
occurs lower than this.
If a user of this site pooh-poohs the need for acclimatization at the elevation of Denver, they should bear in mind that they are young(ish), in good shape, accustomed to sustained physical exertion and probably have often been at much higher elevations.
As for peak athletic performers, according to Sports Fitness Advisor:
Acclimatization to altitude has become an important part of the
preparation process for athletes competing above 1500m (4921ft).
This article later mentions the 1968 Olympic Games in Mexico City and says:
It takes approximately two weeks to adapt to the changes associated
with the hypobaric conditions at 2268m (7500ft), roughly that of
Edit in Response to Comment by @Tullochgorum
The OP did not ask about AMS, but about acclimatization. People in good physical shape, like most users here, will land at Denver and will not notice the effect the altitude has on them unless they have to run a goodly distance to make their connection. So they might pooh-pooh the idea of an effect in Denver. In contrast, the effect on someone in poor shape might be very noticeable (needs assistance at Denver airport, doesn't need assistance at Dulles) and a top athlete might be so attuned that he might notice any effect immediately.