Is this contradictory or in some way contrary to the spirit of the tags in general? If so, it seems like we should enforce some kind of rule that a question with system-agnostic should have any system-specific tags removed. If not, then it's simply nice to know.
The problem here is that system-agnostic wears a lot of different hats. system-agnostic has come to mean a lot of different things to different people at different times, and whether or not it can be combined with another tag depends on what system-agnostic happens to mean at the time.
system-agnostic to indicate a deep question
This is one of the few uses for s-a that even I can get behind. The idea is to have a single tag that someone can click on to quickly get a list of deep, soft, essay-type questions. "System-Agnostic" isn't a great name for a catch-all tag like that, but it's got historical precedent, folksonomy, etc.
For this use, system-agnostic will often mix with other system tags.
system-agnostic to invite non-rules discussion
Suppose you have a kind of soft question you need an answer to. You're using a specific system, and you'd accept something specific to that system. But you also kind of suspect that there's a more general answer and you'd be happy to accept that. So you throw on system-agnostic to say "hey, I'm okay with an answer that doesn't cite rules for this specific system."
I think it says kind of crappy things about us if we need to explicitly tag for this behavior. But maybe those things are true, and at any rate... People do this all the time.
For this use, system-agnostic will almost always be mixed with a system tag.
system-agnostic to refer to system-less, homebrew, and freeform
In very rare situations, s-a is used to refer to questions involving a system that hasn't been published. This is a bit of a misnomer, but folksonomy, etc.
For this use, system-agnostic will almost never mix with other system tags.
system-agnostic as top-level hierarchy
Some people consider s-a to be the top of this hierarchy:
In other words, a question that applies only to Dungeons & Dragons 3.5 gets only dnd-3.5e. A question that applies to Dungeons & Dragons 3.5 and Dungeons & Dragons Fourth Edition only gets tagged dungeons-and-dragons, a question that could apply to both Dungeons & Dragons and Vampire: the Masquerade only gets tagged system-agnostic.
This has always felt a bit redundant to me.
For this use, system-agnostic should not mix with system tags.
system-agnostic as completionism
Some people have the goal of tagging every question asked with a system. So what do you tag a question that isn't system-specific? system-agnostic.
For this use, system-agnostic will never mix with a system tag.
system-agnostic as totem against the people who play shudder that one system
The story goes that there's a barbarous horde of people playing one of the more popular systems (which one depends on who you ask). The theory is that these people will ignore the title, body, comments, system-tags, and answers to a question, but will immediately be turned aside if system-agnostic is invoked in the tags.
Heathens. Don't they know we're trying to talk about roleplaying games here?
Anyway, for this use system-agnostic should be able to combine with anything other than that one system.
If you're playing a specific game but asking for generic advice, I think it's reasonable to tag both system-agnostic and the specific game. That way, you indicate the desire for generic answers while also showing how it applies to the specific system (if appropriate).