tl;dr: current “active” accounts is estimated to be around 1.2 million. 31% of which are “raiders” (including “serious LFR”/clearing raiders). Between 41% and 51% are “M+ players” but some of those are just raiders who do M+ because they feel they have to.
“M+ players” presumably have hit each dungeon at least once. Raider io can’t tell us how many characters have hit every dungeon, but that number can’t be more than the count for the lowest dungeon. For season 2 that’s 2,170,846, for season 3 1,535,245. If you split that up to 15+ and < 15 those numbers are 1,055,165/1,092,357 for season 2 and 898,227/615,353 for season 3.
Wowhead says 18% of “profiles” (accounts?) have KSM for season 2 and 15% for season 3. The total number of WoW players then is going to be: # of KSM characters / KSM characters per KSM account / % KSM accounts. The question then is, how many KSM characters are there per KSM account? I think a reasonably safe assumption would be 3 to 5, so for simplicity we’ll say 4.
At 4 KSM characters per KSM account we have 263,791 KSM accounts for season 2, which being 18% gives 1,465,507 total accounts. For season 3, at 4 KSM characters per KSM account it’s 224,557 KSM accounts, at 15% means 1,247,538 total accounts.
So, currently, by these calculations and with the 4 KSM characters per KSM account assumption we arrive at 1,247,538 currently active profiles, however Wowhead counts profiles.
The next question then is, what proportion of the player base “does” M+? We know the number of KSM M+'rs, so the question is how many non-KSM M+'rs are there. As mentioned above, that number would be the number of players completing all dungeons at any level - the number of KSM players. For season 2 that number was 1,092,357 and season 3: 615,353.
So the problem here is, how many accounts are there per non-KSM character? Some of these non-KSM characters will belong to the KSM accounts, and some of these non-KSM characters will be the second, third, fourth, etc. character of a non-KSM account.
Things get involved here so we’ll do season 2 first then season 3. From above, for season 2 the number of KSM accounts is 263,791. Say half of those have a non-KSM character, so 131,896. So non-KSM account characters are 1,092,357 - 131,896 = 960,461.
Now let’s assume that non-KSM players aren’t as enthusiastic about M+ and they only have 2 characters each that do M+ at all. So then the number of accounts that are non-KSM is 960,461 / 2 = 480,231 non-KSM accounts for season 2.
Repeating that for season 3 gives 224,557 KSM accounts / 2 → 112,279 KSM account non-KSM characters, or 615,353 - 112,279 → 503,074 non-KSM account non-KSM characters, or 251,537 non-KSM accounts.
So for season 2 there were 263,791 KSM accounts + 480,231 non-KSM accounts = 744,022 “M+ players”. For season 3 it’s 256,636 + 251,537 = 508,173 “M+ players” for season 3. Proportionately then in season 2 the M+ player base was 744,022 M+ players / 1,465,507 = 50.8%. For season 3 it’s 508,173 / 1,247,538 = 40.7%.
Now for raiding. We’ll do just season 2 so that we give all the “raiders” time to clear SotFO (and get the achievement). Wowhead says 31% of profiles cleared Sanctum on any difficulty. This number includes LFR so the actual number of “raiders” will be less. Given the number of players from above, the number of raiders in season 2 was 1,465,507, so at most 454,307 “raiders”, again some of which will be LFR only.
What is interesting then is that some proportion of the “M+ players” will really be raiders that are doing M+ for gearing for the raid and otherwise would not be doing M+, so debatably are not “M+ players” at all. Just as a guess I’d say 80% or more “serious raiders” (so excluding LFR-only) would be in that “M+ players” number, though the number of M+ characters per account is likely less for raiders than that for “pure” M+ players.
The numbers vary most based primarily on the number of KSM characters per account (we assumed 4) and secondarily on the number of non-KSM characters per account (assuming about 2.27). The more M+ characters per account, the lower the actual populations.
Edit: added commas, thanks