Does the Third Amendment apply to local law enforcement?
Interesting question.
I think the Fourth Amendment has more applicability here.
There's a simple answer: which reading would give the government more power in a particular situation?
See, the War on Drugs must be fought, and we need the police to be well funded and well armed to do it… just like soldiers in any other war.
Or, they're busting into the homes of people and staying there (traditionally called 'quartering')… but they aren't soldiers, not technically.
And that is how they will interpret it.