Forrest is the one going with the flow, the feather represents that. The movie is not conservative, it's nihilistic. Forrest would have a been religious if the intention had been to give the movie a conservative slant.
The whole movie represents how life makes no gift, life is random events "Life is like a box of chocolate, you never know what you're gonna get.", and Gump represents an empty vase, a person without aspirations, and it sends the message that one without aspirations experiences no sorrow. Gump is the only one "going with the flow", all the others have dreams or are running towards something. That's another message: "Gump can run like the wind", like Jenny said. Precisely, Gump runs to nowhere, while others run somewhere and get punished for it, or others get punished for their benefit.
Bubba had a dream to own a shrimp company; he died and Gump lived his dream instead, without experiencing the joy Bubba would have, reducing Bubba's dream to nullity.
Dan loses his legs at war, gains them "back" after becoming rich thanks to a hurricane that destroyed the livelihood of other fishermen. He even goes on to invest his wealth in that new "Apple" company, just to reinforce to us the idea that life is a big game of chance and Dan is someone who experienced bad luck and good luck.
Jenny is a victim who is trying to find comfort in a chaotic world and ultimately finds none other than with the empty-headed Gump: nihilism.