There are several instances within the script (seen on screen) and the script directions that indicate that the streamers are in fact stars;
Hoshi in Ent: Fight or Flight explicitly states that the movement is caused by stars:
HOSHI: The stars are going the wrong way, sir.
ARCHER: Wrong way?
HOSHI: On both my training tours, I had port side quarters. I'm having trouble sleeping.
Within the scripts
From TNG: Unnatural Selection
BEYOND THE PORTS the stars streak toward us at warp speed.
Rina has a clear view.
RINA: Beautiful, isn't it?
GEORDI'S POV -- He "sees" the ship's navigational shield as a gossamer scrim of shimmering color, and beyond, countless waves of energy bursting from exploding suns.
And from TNG: The Vengeance Factor
MAROUK: A light meal in twenty minutes.
Yuta nods in obedience, but Marouk has already turned away to look out the port at the stars streaking by.
And from TNG: Yesterday's Enterprise
EXT. The ship is traveling at WARP SPEED and the stars STREAK by
And from TNG: Tin Man
INT. TAM ELBRUN'S GUEST QUARTERS (OPTICAL) - TAM is STANDING by the long WINDOW, face half-away from the camera, watching the STARS STREAK BY at warp.
And from DS9: Once More Unto the Breach
The viewscreen shows the stars as they begin to streak by at warp, the crew go about their jobs with a professional precision
And from TNG: The Emissary
EXT. SPACE - THE ENTERPRISE (OPTICAL)
as the probe "pulls up alongside" to starboard as the stars streak past at warp nine.
Obviously the flipside of this is when we see Zephran Cochrane's ship at warp within the Sol system and yet still see star streamers. This can potentially be explained by the presence of interstellar dust interacting with the warp field or deflector fields (which Cochrane may or may not have had). Highly accelerated particles would glow as they suddenly gained momentum.
That being said, the script then disagrees further, referring the the streaks as both "stars" and "warp stars"
As Picard and Geordi are slammed back into their seats and the stars
WHIP PAST the windows in the familiar warp effect.
GEORDI: Dropping out of warp.
Out the front windows, the warp stars STOP... the ship JOLTS
slightly... turns to the left... Earth can be seen in the distance.
A similar effect occurs in TNG: Descent when the ship is traveling at high impulse.