Gentleman:

A most alarming sight, what appears to be rust in the barrels of two rifles. They are thin streaks, so I am unsure if they are really rust, but the color is right. I have some JB Bore paste, and can scrub away (if this is the right thing to do). I also have some cold blueing to re-blue the bore, but again am unsure if this is proper. The advice of those with experience is appreciated.

Probably copper fouling. I have a Savage that is a copper fouling monster. You can see it in the muzzle when the sunlight hits it. It could be rust, but rust will usually result in pitting and is very evident when viewing with a bore-scope.

Get some copper remover like "Sweets" and see if the patches come out blue. My Savage fouls so bad that Sweets nor JB even makes a dent. But it shoots sub-moa, so I guess it doesn't matter.

Copper, not rust. It might not be built up enough to hurt anyhing. If you clean it all out, accuracy might get better, or worse. Cleaning won't do any irreversable harm. Do a search for copper removal. I like the spray foam bore cleaner from Walmart or Gander Mountain. Sweets works, but takes more work.

It's probably copper but not always. I built a 6.5-06 many years ago with a chrome-moly barrel and blued it. It was standing in the corner of the house (never got it wet) and I walked by one day and it was orange with rust. Not copper. Have not used a chrome-moly barrel for a gun of mine since.

You'll know Ferrous-f**king-oxide when you see it. I had rust in the barrel of my 300 Win from a hunting goof (always run a patch through your barrel when you get home, no matter how tired you are). Now there's a rough spot in the bore. I took a friend's advice and JB'd the bejeezuz out of it. We'll see if it keeps fouling or not.