Is there a way to white-list an app (web browser) so Froyo 2.2 memory manager does NOT kill it?
AFAIK, you can't.

But, you can customise when to kill background apps (not selective app) by tweaking MinFree values set by Android (root is required for tweaking). If you have problems dealing with it, there are many apps in Play Store for that. My fav is AutoKiller Memory Optimizer.

And, when foreground app and/or kernel runs out of memory, killing background apps can't be prevented. It's because foreground apps and kernel are more important than background apps. Probably, you'd not be wanting to crash device to preserve your web browser in background.

Update:
Another approach is to create/increase swap memory in device. There are apps for this purpose too: Swapper (by dario) and Swapper 2 (by Elviss).