That's perhaps the best-produced Fleetwood Mac song, which is saying something. Three singers, each triple-tracked, same technique used for Bohemian Rhapsody.
 
I doubt they used externally-sidechained compression on that recording. It just wasn't a common practice in the all-analog era when it was recorded. More likely, it's straightforward aggressive broadband compression from something like a 670 or 1176. And plenty of organic distortion from a classic amp (currently uses Orange, but back in the day it was an Ampeg).
 

 
However, that even-ness is a hallmark of a very good player who can modify his plucking intensity in real time on a note-by-note basis. An easy way to fake it in the digital era is using a dynamic equalizer.

Is he using a pick in that photo? 

Looks like it...Probably a felt one.  Attack without the click...
 

It sure looks like a pick but then the photo might have just caught him dampening the strings. Note his left hand  holding an A and a D at the fifth fret low strings , but his fingers where the pick would be are over the hi strings . Look at his hand position too. That's real close to the bridge which is where I play too. I find the further away from the bridge the less attack you get. You can hit the strings a little harder at the bridge. It's all in the hands that sound. 

Felt picks eh - you learn something new every day.

sharke
However I'm not sure I like the effect, and I try to write bass lines around the kick so that they're not (or rarely) playing together. 

I gotta say, sharke - this here strikes me as a bit of an oddity because my training tells me that kick and bass ought to play together most of the time, since the kick sound would make the bass punch a bit harder.
But I've never thought about it in terms of low frequency-crashing or anything like that, if that's the reason you'd cite for writing bass lines so that they are independent from the kick.
Interesting! Any good examples in popular music of this?

davdud101

sharke
However I'm not sure I like the effect, and I try to write bass lines around the kick so that they're not (or rarely) playing together. 

I gotta say, sharke - this here strikes me as a bit of an oddity because my training tells me that kick and bass ought to play together most of the time, since the kick sound would make the bass punch a bit harder.
But I've never thought about it in terms of low frequency-crashing or anything like that, if that's the reason you'd cite for writing bass lines so that they are independent from the kick.
Interesting! Any good examples in popular music of this?

I can't think of any specific examples offhand, but having the bass play the off beats against a four to the floor kick is very common in a lot of techno and trance music. It was also quite common in disco. 
 
Of course you're not just limited to doing this with the kick and the bass. Writing parts which entwine around each other but never play together is a great technique for achieving a full sounding arrangement without too many things stepping on each other. It's really easy to do if you're programming MIDI in a piano roll - if you have both tracks in the PRV, you can visually see them flow around each other. Arranging like this can greatly reduce the need for EQ as you're not having to carve as much out of each sound. 

This is another great sounding Fleetwood Mac song with amazing production. Again, perfect bass. But everything else in it is perfect too. Very nice balance of frequencies. Brasslike keyboard sound in right channel during the chorus is just lovely. I hated this stuff at the time because I'd grown up with Rumours and I felt like they went all cheesy in the 80's. I can really appreciate how good it is now though. 
 

FM always had top shelf production.
they pretty much set the bar for that style of music, IMHO
 
that said,
so much of this stuff you are talking about,
has nothing to do with production.
 

To my ears, that bass sound (does sit nicely) isn't direct.
It sounds like an Ampeg B15.
That type of amp will smooth things out, you hear a nice round bottom end... but the signal doesn't go down past about 50Hz.  The top end is also nicely "rolled off" in large part due to the speaker.