Nah. It's a fairly apolitical spy thriller mixed with a found family sitcom, with emphasis on character development and repeatedly beating the reader over the head with a message of "war bad."
Not really. At it's core, it's a found family sitcom with action elements. It's cute and fun, but can have a shitty marry and reproduce tone to it (despite being a found family, with, y'know, an adopted child) that anime can kinda do sometimes.
It has a East/West Berlin spy movie aesthetic, but doesn't really pitch either side as the "good guys." The comic writer is an apolitical lib that just likes the setting.
That said, shitty right-wingers also like it and are creeps about the characters.
The family sitcom at its origins is a fairly conservative genre of propaganda like Father Knows Best from the 50s. There's a reason a lot of more comedic sitcoms thereafter in some ways a rejection of the 50s pro nuclear family. Like the Simpsons and Moral Orel at the extreme end.
I only read the bylines of the reviews, sniff, of Spy x Family and it seems like it is comfy at the functional end of family sitcoms. Correct if wrong.
I guess my standards for "is this annoyingly anti-communist" are incredibly low - they at least live pretty normal lives in the East and doesn't have a "gommunism no food no consumer good" thing going on.
You're right, though - Yuri and Donovan Desmond have the "scary badguy" aesthetic.