I'd watch it ...
... through a 4.5 - 14 x 40 Leupold scope for a couple of seconds before pulling the trigger.
If culling preserves our remaining reds then I'm all for culling, just as I support the efforts of those who try and trap large numbers of the invading American Signal crayfish.
Doing nothing is no way of admitting that we made a mistake at some point and it is the very worst form of apathy when discussing the ongoing preservation of our native species.
I consider myself very lucky to live in an area that still enjoys a healthy population of Red squirrels, and I take every opportunity to selectively reduce the greys I spot when out and about. Perhaps my efforts make absolutely no difference, or perhaps they do. I like to think that if others are doing what I am then, collectively, we must be having a positive effect, even in small, localised areas.
A fringe benefit is that squirrel tastes delicious so the greys I shoot are never wasted...