Lets look at this logically.
first of all, the "golden rule" of
shutter speed = 1/focal length was developed for film SLR cameras and having the results blown up to an 8x10 inch print, and remain what was considered acceptably sharp, specifically a similar argument to depth of field, and the blur caused by a point of light in this case moving with a specific circle of confusion such that when enlarged on the 8 x 10 print, it was no bigger than a 1/100 inch dot.
SO, if you apply this to either a cropped sensor, or enlarging the final product beyond the magnification ratio from a 24x36mm frame up to an 8 x 10 inch print, i.e. a magnification of 7.5 for a film frame, or 11.2 (magically 1.5 or the crop factor higher than the enlargement ratio for film) then you have an issue.
from this, yes crop factor does come into it, as does enlargement ratio after you take the shot.
Now, how far can you push the golden rule with shake reduction, well, that depends on how good a photographer you are and how good your technique is.
the first shot in the thread below is at 1/40 of a second on a 300/4 plus 1.7x AF converter (510mm focal length)
https://www.pentaxforums.com/forums/lens-sample-photo-archive/164135-pentax-k...4-samples.html
using the golden rule, this is 4 1/2 stops below the nominal recommended hand hold speed.
and when you consider the 100% crop and enlargement is considerably better than acceptably sharp
shake reduction is effective at all speeds, but it also varies from user to user
this is because there is no substitute for good technique.