Why are red blood cells not attacked by NK cells?
The question states, not quite correctly, that "if they stop presenting anything at all, they will be eliminated by the NKs".  In fact, simply not having MHC is not enough to trigger destruction by NK cells. 

NKs have a two-part trigger. Part 1 is an activator; part 2 is a suppressor. When the activator is present, and the suppressor is not present, then NK cells will destroy the target.

The suppressor is typically MHC class I, which is present on almost all normal cells. That means that NK cells will not destroy normal cells. There are many different activators, but most normal cells have at least one of the activators also present. That means that NKs are normally primed to destroy, but refrain from destruction because they also sense the suppressor.

With that explanation, it should be clear why RBC are not destroyed by NK cells. Even though they lack the suppressor, they also lack any activators. Since there are no activating signals, the NKs don't need to be also suppressed, so the lack of MHC doesn't lead to an attack.

Sample references:


Two-signal requirement for activation and effector function of natural killer cell response to allogeneic tumor cells
Controlling NK Cell Responses: Integration of Signals for Activation and Inhibition


It's also possible that RBC further protect themselves by showing a "marker of self" on their surface (Role of CD47 as a Marker of
Self on Red Blood Cells) but that doesn't change the important point about NKs mode of activation.