Furniture, Wood and Cabinetry Finishing - Staining Pine Trim Has White Streaks

I Have Finished Removing All The Paint From The Wood In My House. The Railing Going Up The Steps Is Pine. The Balusters Are Oak. I Am Staining Everything A Golden Oak. The Pine Has White Streaks Even After Applying Two Coats Of Stain. The Oak Wood Looks Great With One Coat. What Can I Do To Cover Or Get Rid Of The White Streaks In The Pine? Will Putting The Polyurethane Clear Semi-gloss On Help? What Can I Do To Prevent This From Happening To The Pine Upstairs Before I Stain? The Downstairs Wood Is Maple And Oak. Will The Stain Take To The Maple As Well As It Took To The Oak?
Also Will Be Doing The Oak Floors. Should I Remove The Old Stain First Before I Use The Sanding Machine?

Sounds like the paint wasn't completetly removed from the pine. Since pine is a softer wood than oak paint or stain will soak into the wood deeper. I think maybe there was some paint residue left and the stain helped to bring it to the surface. Applying poly won't remove the white.

Oak and pine won't take stain the same so they won't stain the same color when using the same stain. Maple and oak are also likely to stain different. While different speicies of wood can be colored to look similiar, different woods will stain diferently.

Is it possible to camouflage the white? it would be a lot of work to restrip the pine.