This is an interesting question. My gut reaction was the same as P@nther’s - that the territories of a friendly power would not be friendly while your power is neutral. This makes sense from a point of view of the dictionary definition of “neutral”, but not everything in war makes sense. Let’s look at the relevant rules.
According to the definition of “friendly territories” on page 8 (Europe Rulebook), they are “controlled by you or a friendly power”, while the definition of ‘neutral territories" indicates that they’re “not controlled by any power, or controlled by a power on the other side with which you are not yet at war”. Further, the definition of “neutral powers” on page 15 states that powers on the opposite side of neutral powers are not yet enemies, but it doesn’t say that powers on the same side are not yet friends. This seems to lump territories controlled by a power on your side while you’re neutral into the “friendly” category (though you’re explicitly prohibited from going there while neutral). This is reinforced by with the explicit restrictions on the movement of neutral powers’ units (rather than simply declaring all other powers’ territories neutral while you’re neutral).
The upshot is that the territories of a friendly are technically friendly while your power is neutral, but they’re pretty much treated as neutral for all practical purposes. However, they do meet the requirement of being friendly since the start your turn once you’re at war.
From a thematic point of view, while the US or USSR might be officially neutral, the old adage “the enemy of my enemy is my friend” still applies, unofficially. While a neutral power can’t do anything to provoke a power on the other side, such as openly aiding another power, it can still be prepared to join the war at a moment’s notice. This took a little digging to sort out, and it is a little counter-intuitive, so it’s easy to come to an incorrect conclusion when “shooting from the hip”. I didn’t think through all of the ramifications of this situation yesterday when P@nther asked me about it. Sorry for any confusion this may have caused!