Talk to be about the effects of pickup height

I’d love to get @Turnaround ’s advice on this one.
IMO many players have their pickups too close to the strings. You get more output that way but at the expense of a couple of things.

First, as has been mentioned, the magnets can interfere with the string vibration if too close, and that causes a warbling effect.
Second, if you are playing around the 12th fret and upward, there are a lot of overtones in the string's vibration which are exaggerated when the pickup is too close to the string. Backing off the pickup height will emphasize the overtones less and will sound cleaner (if that's what you want). I always start with the pickup poles 1/8" from the string when fretted at the last fret, listen to the result and adjust from there.
 
Adding to @Turnaround's excellent advice, now you see why you only check pickup heights/clearance with the strings fretted at the very last fret: Do it with the strings unfretted, you'd never hear the overtones in the upper frets.

Also, on any single pickup bass, begin playing directly over the pickup. Keep playing but move your picking hand slowly towards the end of the neck and the sound gets fatter and bassier. Start over the pickup again, but keep playing while slowly moving your picking hand towards the bridge, and the sound gets brighter, loses some deep end slowly, and gets twangy right near the bridge.

This is a whole 'nother tone control. This happens on any bass, but not nearly as obvious on two pickup basses in many cases, but on a Precision it can be very useful, and works with any and all strings and any tone/amp settings. Subtle in most cases, but worth remembering and using.
 
This thread here answers most of my questions. I play active EMG J Basses mostly. I just installed a set of EMG passive Geezers in my P. I'm not used to the lower output.Currently I'm at 2.5 mm on the G and 3mm on the rest. I would like to move them a bit further away so I can pluck the high strings with my fingers easier when I do Palm muting. My G string is much quieter than the rest. If I did 4mm on the G and 5mm on the rest, would that make the bass sound wimpy and less punchy or just quieter. Or is that still a reasonable distance? I'm asking here first because I might have to change out the foam underneath to try it.
 
IMO many players have their pickups too close to the strings. You get more output that way but at the expense of a couple of things.

First, as has been mentioned, the magnets can interfere with the string vibration if too close, and that causes a warbling effect.
Second, if you are playing around the 12th fret and upward, there are a lot of overtones in the string's vibration which are exaggerated when the pickup is too close to the string. Backing off the pickup height will emphasize the overtones less and will sound cleaner (if that's what you want). I always start with the pickup poles 1/8" from the string when fretted at the last fret, listen to the result and adjust from there.

Definitely excellent advice, and I'd add that, with J pickups with flush poles, having pickups too close to the strings can produce poor string-to-string balance, and the smaller the fretboard radius, the worse it's likely to be. (I know the OP has a P pickup, but the thread title is more general.)

On two of my J-basses, I've needed to lower the pickups from factory settings to get decent string-to-string balance, even with relatively flat 12" and 14" radius fretboards.
 
Actually the j bass part is interesting to me as well. I play mostly Jazz Basses 5 string, many of them have EMG pickups, the standard ones that have a bar magnet underneath and also the jvx ones that have pole pieces. EMG. says because there's less magnetic pull on the active pickups I can get closer to the strings so I have them between 3/32 on the g and also on the b string.
That tends to work out to be 4/32 on the 4 string.
Passive P bass pickups even though they are emgs, buy something that I don't know much about.