I have had to use a long steel bar and a pedal spanner too many times to remove pedals that have had white grease on them on bikes built up elsewhere, you can see the solid crap that comes back out of the thread once you get the pedal out, same with seat pins, white grease welds them in place.>Never use white lithium grease on pedals.
I'd be curious as to where you got that from.
Pretty sure I used to use it pretty much universally years ago, never had a problem...and a brief web search just seems to throw up somethin akin to an old wive's tale/mtb mag waffle. Castrol LM - typically lobbed in wheel bearings and I've also used for years - is a lithium grease.
The white stuff is a bit thin, tho'
Threadlock's worth putting on things you really don't want to come undone in a hurry, such as disc rotor/caliper bolts but I don't bother/seem to need to use it elsewhere.
I think there's a few cases where copaslip's a better choice, istr summat related to titanium frames...
Brown grease comes in all kind of weights, even the lighter stuff does not mess up a perfectly good bike the way white grease does.