The Cap costume is admittedly one of the more outlandish ones, particularly given his origin. Though he's going to be wearing the Kirby-ish one in the USO show, just as a demonstration of how silly it would look in real-life, apparently.
No more silly than Spider-man, Batman or Superman. No one going to see this movie should be expecting
Saving Private Ryan.
Honestly? It is sillier, and (sadly) that's mainly due to the American flag motif. Some time (I'd say around the late 1960s,) that sort of blatant patriotism began to be perceived as corny, un-hip, and smug (see the Colbert Report intro for an example.)
Then there is the complication that - correctly or incorrectly - the American flag is perceived in some corners of the world as a symbol of arrogance and/or imperialism. So you've got a double hurdle to overcome: younger Americans who may laugh at the uniform, and foreign audiences who may scoff at Cap's All American hero image as a false reflection. Maybe none of this matters to comic book fans, but it does matter to a studio trying to sell tickets to all the non-fan moviegoers.
This is why the WW II setting makes a lot of sense; it grounds Cap in the period when it was perfectly credible to dress a guy up in a flag themed soldier's outfit, for propaganda purposes. No, I don't expect
Saving Private Ryan, but I do expect to see some grit (and yes, blood) in the fight scenes. That stuff about some people snickering at the American flag? Funny thing, when that flag appears (properly done) in the middle of a battle scene, torn and ragged with chaos all around, it stops being corny. That's what I'd like Captain America to evoke.