appears to be an Egret feather
a long plume (especially one of egret feathers) worn on a hat or a piece of jewelry in the shape of a plumea rather prized feather, Native americans wore them.
They were so sought after for hats and the like throughout the years, that an Egret feather became the symbol for bird preservation as the egret populations declined.
I believe the white feather your story is talking about is ... a common "Chicken" or "Gamecock" feather.
There is also an alternate meaning...
PacifismIn contrast, the white feather has been partially embraced by pacifist organisations as a sign of harmlessness. During the First World War the pacifist Fenner Brockway received so many white feathers he was known to comment that he now had enough feathers to make a fan.
Some time after the war, pacifists found an alternative interpretation of the white feather as a symbol of peace. The story being that in 1775 Quakers in a Friends meeting house in Easton, New York were faced by a tribe of Indians on the war path. Rather than flee, the Quakers fell silent and waited. The Indian chief came into the meeting house and finding no weapons he declared the Quakers as friends. On leaving he took a white feather from his quiver and attached it to the door as a sign to leave the building unharmed.
The story may not be true, but in 1937 the Peace Pledge Union sold 500 white feather badges as symbols of peace.
In 1985, progressive rock band Marillion released a concept album entitled Misplaced Childhood, whose final track, White Feather, was an explicit reference to pacifist idealism.
When I hit the streets back in '81
Found a heart in the gutter and a poet's crown
I felt barbed wire kisses and icicle tears
Where have I been for all these years?
I saw political intrigue, political lies
Gonna wipe those smiles of self-satisfaction from their eyes
I will wear your white feather
I will carry your white flag
I will swear I have no nation
But I'm proud to own my heart
I will wear your white feather
I will carry your white flag
I will swear I have no nation
But I'm proud to own my heart
My heart, this is my heart
We don't need no uniforms, we have no disguise
Divided we stand, together we'll rise
We will wear your white feather
We will carry your white flag
We will swear we have no nations
But we're proud to own our hearts
We will wear your white feather
We will carry your white flag
We will swear we have no nations
But we're proud to own our hearts
These are our hearts
These are our hearts
You can't take away our hearts
You can't steal our hearts away
I can't walk away
No more
Surprisingly the white feather doesn't appear to be associated with the dove of peace.