Well, the common-sensical thing is that you guys need a band meeting where you talk about what's expected of everyone. If he's not willing to do what's expected of him, then you need to find someone else. OBVIOUSLY, do not do this when you've got a gig on the slate and may not be able to find a replacement in time.
And you really should have gone over that kind of stuff before the band even started. I have a whole big checklist of points to go over with any bands I might be joining, before we ever play anything together--because if that ideological stuff isn't agreed upon, then it's pointless.
Just speaking as a drummer with opinions on this stuff, for a tribute band, I would want the band to have the same line-up as the band we're recreating, as well as a similar look, similar instruments, similar mannerisms, etc., and part of that would be expecting everyone to learn the songs so that they could play them just as the original band did--which could include not always playing them the same, depending on the band (for example, a Zeppelin or Allman Brothers or Grateful Dead tribute band wouldn't always do tunes the same). I'd only be interested in this, by the way, when the original band is no longer around, or when we'd be recreating a period that the original band no longer bothers with (for example, say we were doing an exclusively 80s-Kiss tribute band).
For just a plain old cover band, however, I'd want to make the songs "our own", which would mean NOT just playing them like they are on the records. I'd have an approach more similar to your drummer's--I never learned anything note-for-note for cover songs when I was in cover bands, and as a matter of fact, I HATE when the actual bands play things note-for-note live. If you played something like "Talk Dirty to Me" very different on guitar, I'd prefer that. When I'm doing originals in bands, I do the same thing. What I played on a record isn't going to be what I'm playing live down the road. I don't even remember exactly what I played on records, and purposefully so. I like songs to gradually evolve over time.
From your descriptions, it sounds like you're somewhere between a tribute band and just a plain old cover band--because you're not just recreating everything about a particular band. So I'd probably take something of a middle approach, too. As long as we're doing things that are characteristic of the genre, I'd not expect everything to be note-for-note. I'd probably want to move to more of almost a parody direction with it, actually, but that's just me.
Anyway, obviously not everyone has the same approach, the same ideas about this stuff, which is why it's imperative to discuss it from square one. It sucks if you guys can't come to some agreement and you really like the drummer personally/he's a friend, but unless you're just doing something as a casual hobby, the band is a business, and business needs to come first in that situation.
However, if he's really a good friend, also consider whether you think the drummer's approach is hurting the band's business (and taking into consideration what you're trying to achieve as a band)--is your attendance and word-of-mouth not what it could be because of what the drummer is playing? If it's not really affecting audience opinions, maybe it's just the guys in the band being persnickety about it when it's not really that big of a deal. You'd need to try to talk to some random folks in the audience about what they like and dislike about the band to know. It might be a good idea to get a crew member, manager, or even just a friend, etc. to mingle with the audience after you've played some. Have them pose as just a normal person there to listen to the band. Other folks are more likely to give honest opinions in that case.