It is important if you want to classify national team matches. Whether you like it or not, FIFA is the authority for association football.
Yet there have been matches played between (at the time) non FIFA members FIFA also recognizes as official A. I don’t mention the pre 1904 internationals, but i.e. some matches played by Hungary before they gained FIFA membership in 1907. The 1920 Olympic Games match Sweden – Greece is listed as official A-international match even though Greece became FIFA member in 1926.
If countries are FIFA member or not is not important. If they want to play against each other they can also do without FIFA.
I do not agree; it is not about your buddies playing a match but two countries...Anyone agrees China was a country and they played full internationals in the sixties against teams like Mongolia, N.Vietnam, etc....none of them was a fifa member. At the present times almost every country is a FIFA member , so today the problem is different.
Regarding this topic you are right by saying it is not a match between buddies but between two countries. I think nfm means the same on his post. A China – Mongolia match will be the same match no matter if they are FIFA member or not, no matter if FIFA is involved or not. Both sides will field the same team, play at the same ground with probably the same referee and linesmen under the same weather conditions.