Like most people here, I have been an avid Civ player since Civ I, and I have to say Civ V is such an abomination compared to cIV BtS expansions, not to mention the worst of the series by far.
I believe I can speak for the majority of the Civ players here regarding features that absolutely must be brought back to Civ V, hopefully in future patches or expansions. These features are so essential to the whole Civ experience that I am not sure why Firaxis removed them in this generation.
No, you don't speak for the majority of Civ players here or anywhere. That's hubris and arrogance.
1. We want our stack back: 1UPT makes moving units around so tedious and it's hard to get into formations in battle.
No. Hell no. Part of being a good General is getting there "firstest with the mostest". The engaging tactical combat is far, far superior than the old Stack of Doom. Perhaps you just need to get better at it.
2. We want the old strategic resource system back: who came up with the idea that one iron mine can only generate one swordman? If I have an iron mine, I should be able to put it to use and build as many iron units as I want.
No. This prevents spamming the super-unit of the age and forces you to think of force composition. I love having to consider my force makeup - do I use that iron for a swordsman or a ballista? Resource limitations are a real-life consideration and I think the abstract implementation of it in Civ V is awesome.
3. We want our slider back: the ability to shift the macro focus of your empire to either wealth/science/happiness is more dynamic than the current system.
No. I have sliders in each city and the global weath/science/happiness dynamic is dead. Let it stay dead. Again, I'm forced into having to make real decisions on a city-by-city basis. Is it more important to get gold or to build up my army quickly? I don't see anything gained by trying to bring back the macro focus.
4. We want local happiness back: CiV's global happiness system makes the game MUCH shallower, it's like playing a game for 10-year-olds.
No. If anything, it makes for a deeper experience. Before, you could have cities unhappy and it didn't impact your empire - those cities could just "take up land" and they didn't really impact your empire much. Now, if you ignore them they'll spread dissension throughout your empire and can really hurt you. It's an entirely different strategic consideration.
5. No more purchasing units/buildings plz: it makes no sense to buy a building and it's suddenly there the next turn. Firaxis please remove this feature. Realistically, gold should haste the production process, but not producing things out of thin air.
No. Consider it outsourcing.

Actually, I think it fits fine in the current game. I'm not forced to keep a large standing army and can raise one quickly. I can spend a lot of dough to bring a city up to par quickly rather than wait umpteen turns for it. At the same time, there's never enough dough to go around.
6. We want religion back: religion is what makes cIV a much deeper game than all others in the series, including ciV. Why did they remove religion?
Perhaps, but only if they improve religion. It shouldn't be the end-all-be-all of diplomatic relations that it was in Civ IV.
7. Bring back the graphics of cIV: as many players have noted since the game's release, ciV's graphics is absolutely terrible. Rivers and trading posts are just plain ugly. It's just about on par with Civ III if you ask me.
No...and get glasses because there's something wrong with your eyesight.
8. We want the old map grid back: sure, hexes are interesting at first glance and seems to make the game look complicated (reminds me of a boardgame), but after several games they begin to get on our nerves.
No. Hell no. The hexes are great and add a ton to the combat considerations.
Firaxis, please pay more attention to what we the core Civ players really want. Until these problems have been fixed, I'll stick to my cIV.
Hmmm...as someone who purchased Civ I close to 20 years ago, I'd say I'm a core Civ player. What you described above you already have in Civ IV. So go play Civ IV. No one is stopping you and I consider Civ IV + BtS to be the best TBS game of all time. It took 3 years and 2 expansions to get it there, but it's awesome.
With that said, I love the new direction of the game. It is what
this core Civ player wants. It's a new direction and while it has some rather rough edges at times (tactical AI, diplomacy, pacing, religion), I'm glad that Civ V isn't a graphical update of Civ IV like the various Madden games throughout the years. This version feels fresh and new, unlike some prior Civ versions. So you go play Civ IV and have fun...meanwhile, I'm playing Civ V and having a blast.