Tennis absolutely is nationalistic, depending on the player and the nation. Roger and Rafa's fan bases transcend nationalism, but there are many countries for whom a tennis player's nationality is huge. Also, the US where u live does not have much of a tennis presence for the last 20 years on the men's side. And the sport is simply not big in the US, very different from other countries particularly in Europe.
While I don't agree with you that tennis is "absolutely nationalistic," I take your point. Serbia has risen as one behind Novak, one of their most prominent figures in sports and beyond. All of Australia, practically, stayed up, by all accounts, to watch Ash Barty win Wimbledon. It makes a difference how important tennis is to your country, and how many options you have for figures who play on the international stage. In a smaller country, or in a country where tennis has a huge history, like Australia, a transcendent tennis star can. Wozniaki was a hero in Denmark. Murray brought the men's Wimbledon title back to Britain. These players do inspire a certain nationalistic fervor. But tennis does remain an individual sport. People like or dislike Nick Kyrgios because he's the player he is, not because he's Australian. The French might back most of their own, but they've kicked Benoit Paire to the curb because he's a shit-head, and no amount of being French endears him, even to the French. Everyone pretty much likes Barty and Swiatek, and Auger Alliasime and Berrettini, even though most of us are not Australian, Polish, Canadian or Italian. Style of play and personality come into it, too, and I think most people care more for that than the flag they fly. I actually find it a bit weird that tennis players are claimed to a country at all. If it's not the Olympics, or Davis Cup/Fed Cup, or a few others, what does it matter?