It depends on the people who settle Russian Alaska, and under what circumstances. Is there a gold rush? Alaska might be pretty much self-governing, due to the vast distance, leading to a very limited sense of loyality to the Tsar. If Alaska is populated by poor miners and fisherman, they may well pick the Reds over the Whites. Especially if the distance also means that they aren't subjegated to all sorts of ideological purges.
On the other hand, the Russian Far East IOTL became a holdout for the Whites. That was mostly because it was the last place where they could flee to after the Reds began winning, however. Would crossing the pacific and fleeing to Alaska be a viable option for the Whites? If so, you'd likely get White Alaska.
So, basically, it can go both ways.
The US isn't gonna want a communist nation bordering them and neither would the British/Canadians.
Keep in mind that the USSR wasn't really considered 'the enemy' until the end of WWII. If the Reds manage to get entrenched in Alaska early on, the USA and Britain/Canada are going to be cautious, but it doesn't mean they'll invade and annex. They'll want to do that come the 1950s, but by then it may be too late. Stalin will see it coming, and bolster the Alaskan defences. On the other hand, it will be one more reason for the Americans to decide they
really have to destroy the USSR before Stalin gets atomic weapons.
So... Red Alaska might very well mean WWIII following WWII pretty closely (several American generals, including Patton, MacArthur and LeMay wanted this, seeking to eliminate the USSR before they went nuclear).