The core of an RPG game is an RPG system of rolled challenges versus skills/level/stats. Then layered on top of that is everything else that is typically something from other games. Some people will say story. But story without an RPG system is an adventure game. Some people will say combat but combat without the RPG system is a tactical game. Some will advocated for more simulation like gameplay, although this one is probably more modern it does harken back to some Ultima style stuff.
Most Old School cRPGs have a significant amount of both of those or in the case of some roguelikes; just the combat part. Therefore most people tend to identify that both of these are part of the "core" of an RPG. But they are not in reality as we have classic example of cRPGs that lack either one. Personally I am fine with a pure dungeon crawl with negliglible story and I am fine with a game with a great story and a only servicable combat system.
The only thing that can really be said reliably is that the core aspect of RPGs, the rolling/advancement/gear systems are never standalone because they are incomplete or at the least have too little meat on the bone.
In theory you can have an RPG that has no combat at all and its simply a game of stealth gameplay and lockpicking and looting. As long as the stealth and lockpick have rolled checks and the player has a way to build out the capabilities it would be an RPG, that sort of gameplay itself could of course be considered an extention of tactical combat play as you would need some sort of patrol style actors so that stealth made some sort of sense. Or you could have an RPG that was purely based on conversations which were a combination of puzzles and RPG rolled checks that could reward with XP and loot and truly have no tactical system at all.
So it could be said that what we are seeing as far as the general non-agreement is concerned is the fact that we have various RPG systems created and then melded into other game style and in fact we have always had this from the very beginning, but we are seeing even more nowadays where FPS and Action style games are also blending in. We then get a vast morass where people can't agree as an RPG system could be blended in with Adventure elements and one of Action, FPS, or Tactical gameplay. In the past cRPG all had some amount of tactical combat gameplay to put enough meat on the bone of the game and because most were influenced by table top systems which were combat heavy.
Personally I would say that the blends of FPS and Action should not accurately be called "pure RPGs" as the either aiming skill or action/platforming skill is necessary for winning the games and the RPG system while sometimes very strong in gameplay effect is secondary in the interface. However one could make a similar argument with tactical combat gameplay in that for very good combat oriented RPGs you need the requisite thinking oriented skills. Many roguelikes require fairly elaborate planning and tactical thinking gameplay, you don't win TOME4 on Madness difficulty by running up to everything and bashing it because you have great RPG stats/items or you just die fast and lose. So perhaps this differentiation that I have does not really hold water.
Anyway I think the non-agreement comes from expectations of the first crop of cRPGs and the original table-top games which tended to, in a general sense, blend aspects of both Adventure and Tactical Combat gaming into RPG systems of some sort. However even in the earliest examples we absolutely must admit to ourselves that there existed significant games that mostly lacked one of those. The easiest example is Rogue which all roguelikes are named after, this game is one of the earliest of cRPGs and lacks any real significant Adventure gameplay. Later roguelikes such as NetHack and ADOM add significantly more Adventure gameplay. And within the roguelike community you see fairly real divisions for people who like "Hack-likes" versus people who prefer a rogue-like such as Dungeon Crawl (Stone Soup for current builds). The people who are mostly about tactical combat will gravitate to Crawl, people who enjoy something with more Adventure-ish elements will gravitate to some for of "Hack like".
So we have, from the beginning, a confusing set of expectations. In most people minds the "classic RPG" is something like, for example, Ultima 5; a real and meaty combat system and an equally real and meaty world populated with free-form adventure style gameplay. But also from the beginning we really had many games that did not entirely meet this expectation. Now as things have moved on we see some games with adequate tactical aspects but huge emphasis on story like Planescape or Arcanum and then we start to see a heavy emergence of Action blends and FPS blends as well.
So we have gotten to a point where even though things were always somewhat murky and inconsistent, we can't really ignore the outliers in favor the expectations of the "classic cRPG". But many people still have this idea of a RPG system blended into roughly equal parts of story and tactical combat (or at least some kind of combat) and even worse people use RPG to designate all of them.
I would say it would probably be best to simply stop using RPG as a genre term entirely. I would say this as the RPG aspect is not really a standalone genre rather it is essentially a sub genre of many other genres and or hybrids. It is no longer even the case the "classic cRPG" is in the majority of game and the term "classic" is misleading anyway due to game like Rogue which certainly a classic on the RPG scene.
So what we have is people with varying preferences for OTHER genres saying an "RPG" is a bad RPG because its not a good representative of a different genre they like. This is just people saying the same thing in confusing ways because its all essentially defined in contradictory ways.
Some people who like Adventure style gaming and have a little care about combat or are able to tolerate OK combat will say games like Arcanum or Planescape are great RPGs. In reality they are saying they are great open ended Adventure oriented stories. Others who demand good tactical systems will say those two games are mediocre RPGs, but are really saying they are medicore tactical combat games but automatically fold this into the idea of what a "classic RPG" is. Compounding this to make it even more confusing is the RPG systems themselves since a poorly designed system can make the combat or the adventure gameplay seem considerably worse and people often don't separate this, i.e. for example overpowered RPG builds can make the combat system appear much worse than it is or poorly designed lockpick can interfere with adventure gameplay etc etc.