Common sense? So what? Are you really saying you would make a ruling based on not wanting the blue team to get upset with you (and the crew)?
Do you have a rule reference?
So, here we go with the "common sense" vs. "rule" argument. Color me old and grumpy, but I see one major flaw with the argument. It goes completely against 4-36. Yep, one team got screwed out of a score because the official made the mistake of blowing the whistle when they should not have. Too bad - there's a rule to fix that. Once they feel the heat, I'll bet they don't do that again.
So, you give the ball to blue because they might get upset? If I'm white's coach, I'm really going to get upset that you're compounding a screwup with completely ignoring a specific rule. You're going to be getting heat one way or the other, so why not get it right one of those times? And if the heat's too bad, there's a rule to fix that as well.
Look, I understand the issue of rec leagues, camp situation etc. And, if the whistle happend so close to blue getting the ball, I would have no problem with blue ending up with possession. But as I read the OP, the whistle sounded well before blue ended up with it, so white still has team control, and white will have the throw-in.