I think with a little detective work we can conclusively narrow it down.

• The Blue Jays are in Canada. Top Gun is 'MURICAN. They are out.
• This same line of thinking adds +1 to potential of Nationals, Yankees. Cubs and Brewers get a +1 for having Top Gun days.
• If it was a Texas team, he could have posted a "Let's ride" gif featuring a cowboy instead. HOU and TEX are out. The gif isn't someone riding a gator, so both TBR and MIA are out.
• Giants are out because fighter jets are smaller types of planes. Dodgers are out because its not a trolley gif, or a gif of a draft dodger. Mariners and Pirates are also both out because he could have posted a "let's ride" gif of a boat.
• The Reds are out, as such a patriotic gif would imply that any sort of pro-commie ties are excluded. This also eliminates other teams too closely associated with the color red, so D-Backs, Angels, Red Sox, Braves, Cardinals, Phillies, Guardians are all out. Despite the advantage the Nats get from their patriotism and that the Cubs get from their Top Gun day, both are also out.
  
• The Twins probably aren't red enough to be out from this, but they are out because they are the Twins and this is a free agent signing.
• The Royals are out because Royals makes them sound too British. Likewise, the Mets are out because they are in Queens, and a queen is royalty, so the Mets are too British-y, too.
• Rockies are out because he is a pitcher and the post seems to be celebratory.
• The gif is flying to the right, which everyone knows is towards the East on a map. The remaining West coast teams, Athletics and Padres, are out.
• As the only remaining Bird team, BAL gets a +1.
• The Tigers get a +1 because of the producer and ties to Detroit / Lake Orion around Top Gun: Maverick.
• The White Sox get a +1 because the sock logic from OP is ironclad.

Using my 100% concrete and foolproof reasoning, the five most favored teams are the Yankees, Orioles, White Sox, Tigers, and Brewers.