My Knowledge of squirrels is rather out of date, but. with that in mind.
Red squirrels aren't native to America, And the decline of Reds in the UK is partly down to Parapoxvirus which the Greys (introduced to the UK in the 19thc) carry but are largely unaffected by, It kills Reds.
Part of the reason why Reds are hanging on in some places is probably food competition. Greys outcompete reds in deciduous woodland, but reds outcompete Greys in conifer woodland e.g Greys can apparently eat unripe and ripe acorns, but reds can only eat ripe acorns, so by the time acorns become available for Reds, the Greys have already eaten large quantities.
In the less productive fir woodland, the smaller reds have a small advantage, and as far as I am aware, it tends to be areas dominated by native pine (e.g. Scots Pine) forest that are holding onto the Reds.
Greys still eat conifer seeds, but prefer the larger seeds associated with broadleaf trees ie more energy for the same (or less) handling time .
Approximate daily energy needs of a red squirrel is about 60% of the energy requirements of a grey squirrel.
Greys are also actively culled in some areas where they are threatening native Red populations.