The caps seen in the award ceremony are the same as those being worn by differently-uniformed troops opposite, in khaki. It certainly seems like these are an element of the uniform. I'm going to dive out-of-universe for a while but the in-universe conclusion is going to be that since they're wearing these clothes in an official context, surely the hats are part of their uniform - even if there is no full canon explanation of exactly how the uniform design was reached in-universe.
The Star Wars uniforms in general were mostly designed by John Mollo according to overall vision from George Lucas. Part of the mandate was:
George wanted the Empire to look like fascists, and the rebels casual Americans.
(interview with Mollo in Starburst, 1981)
Mollo's contemporary sketchbooks and notes show an enormous amount of research effort into historical uniforms, cost considerations, and back-and-forth with Lucas. I did not buy these notes for £125,000 from Bonhams, but they put many digital images online. For example, he records a query on p214:
Discuss Rebel Troops + Generals - Are those in space craft at the beginning the same as the Rebel Rangers
and a further sketch confirms "Rebel Rangers" as the working name for the people with helmets and waistcoats, alongside other uniform variants labelled "Marines" and "French". Those patterns are recognizably what made it to the finished film, seen in the ceremony pictures.
The note "own shoes" demonstrates some budget considerations for outfitting a large number of background extras; and "Bermans" refers to the theatrical costumier now part of Angels Costumes, who had not only a large stock of uniforms to hand, but also undertook tailoring work for the movie.
What we see overall from the sketches is that Mollo was keen to include the "baseball cap" element as part of the Rebel paraphernalia, probably as a subtle means of making the outfit seem a little more American. This was revisited for the snow troopers in the next movie, who have a similar brimmed cap but with goggles and hoods. Caps of this design, known in the military context as "patrol caps" or "field caps", were in active use by the contemporary U.S. forces. To audiences of 1977, and coupled with the rest of the outfit, they are not incongruous as a uniform element - people wouldn't be wondering whether the Rebels are about to play baseball.
The query above, over how the crew of Leia's diplomatic mission are apparently dressed the same as the Rebel fighters seen later, also relates to practical concerns. In the context of film-making, there was probably some pressure to reuse them in order to create a visual link back to the opening scene, and avoid the expense of another distinct outfit. It creates a little story problem in retrospect for how brazenly Leia is claiming to Vader that she has no Rebel affiliation, but such are the tradeoffs.
Out-of-universe, the most likely reason why some of these troops are wearing the wrong cap is simply the same kind of filming and budget consideration. The online sketches don't seem to combine the soft cap with the "Rangers" ensemble. Maybe, on the day, they just didn't have enough helmets, or the director wanted a little more visual variety.
Once the number of Star Wars properties expanded beyond 1, we see a lot of reuse of visual elements in order to communicate succinctly to audiences. Future Jedi are seen wearing Tatooine desert robes, because that's how we remember Obi-Wan. It's not surprising for the artist of a 2003 comic to pick up visual elements from the 1977 movie, even if they were picking up on a slight accident.
Back in universe, one wants some sort of canon-based explanation for what is going on, just as with the Jedi robes. The standard answer for why the same uniforms appear on Leia's ship and on the Rebels is that the Rebels copied the Alderaan consular uniform. Wookiepedia cites Star Wars Helmet Collection 20 for the proposition that
Due to its simplicity, the consular security uniform was also used as the apparel for many Rebel troopers after Rebel commanders recognized the advantages of establishing a standard outfit for the Alliance Army.
The most direct in-universe explanation for "why are those people wearing those hats" is that those hats are indeed part of the uniform. This is in the context that the Rebel Alliance is a ragtag force of multiple origins, who don't possess a single standard uniform or the means to equip everyone with it. High-ranking officers seem to wear more or less whatever they want. It could be that Alderaanian diplomatic security already offered the soft cap option (as real-world uniforms do, because not everyone wants to wear a huge helmet all the time), or that it was borrowed from a different uniform when the Alderaan design was adopted by the Rebel Alliance. Either way, to the extent that the Rebel Alliance has uniforms at all, these hats are surely part of them: anything you manage to keep on your head during a military award ceremony can only be something your commanders let you put there.