I have to put this to rest. Let me first say that I've been first and foremost a Nintendo fan but I am an avid owner of Playstation products since the PS2, and Xbox since the 360. So I'm not some Nintendo fanboy that thinks Nintendo can do no wrong. They have done wrong, they have made mistakes like any other company. So for me, I have no issue identifying all the crap decisions they've made in terms of past hardware and software.

But however, in recent news, most notable the IGN discussion, the internet has blown up about Nintendo fans and what games they invest in. Comments were made about how Nintendo fans don't buy 3rd party games. I disagree with that, I say that they don't buy western 3rd party games. And of course it goes even deeper than this. Of course games in Nintendo's target demographic, made by western developers, do really well (i.e. Rayman Legends, Minecraft, etc.) But the western 3rd party support that Nintendo has recieved, the games generally don't perform well.

However, I've encountered several people that still believe that the average Nintendo fan buys western 3rd party content. If that were true, I think we'd see those titles perform much better on Nintendo consoles. And of course, we can say that the Nintendo platforms get gimped versions of these games and that's why they don't sell that well, but then the same people will turn around and tout Wii and how several call of duty games sell millions of units. There's like some odd double standard going on here, but more than anything it boils down the the fact that this isn't so black and white. There's a lot that goes into support from a developer, and if a developer recieves a decent enough return to continue supporting a device, especially if the device requires more input due to its lack of modern attributes. 

I guess my thing is, Western developers can develop for Nintendo platforms but, has the damage already been done by that point? Are they willing to downgrade their vision to make a game that might not even sell well? There's so much to consider. In the case of DS and Wii, the consoles were so successful that if you put a decent game on either platform, it would give you a nice return and sell rather well. And that's what I think it comes down to. If Nintendo platforms are highly successful, western 3rd parties will take interest and their games might sell well, like Activision and Ubisoft experienced during that golden era of Wii and DS. 

Then again, you have to think, take away the success of a console. A console like Gamecube or Wii U for example. Those consoles aren't as successful as other Nintendo platforms. And the western 3rd party sales drop off, very badly on those platforms. Where are all the people who bought call of Duty on Wii right? I thought that they'd support western 3rd parties from Wii to Wii U! You see how this thing is just so twisted as can be and people are making conclusions off of it! It's very confusing to me.

My hypothesis? If Nintendo consoles are successful, than western 3rd parties have a higher chance of selling decent amounts of software. And that's really true with any console the truth be told. 

Nintendo fans, do you even care about western 3rd party games like FPS and Sports games? What do you guys think?

Short answer not as long as Nintendo will release a new gen mid current gen, while the console is under powered, compared to Sony and MS is console. The Switch will probably receive a decent amount of third party support at launch. But big titles like Mass Effect and the new elder scrolls will always be played more on PS and Xbox, because A The games will run better or/and more beautiful on these systems.
B The people who want to play third party titles have abandoned Nintendo home consoles since the GC era.
C The Nintendo Switch will primarily be used as a handheld or a secondary console which is purchased mainly for the Nintendo exclusives.

If Nintendo is going to release a console on par with what PS and Xbox offer in the same launch window that might change. But as long as those consoles are vastly more powerful and released earlier I don't think many people will switch from them to a Nintendo console for third party games.

Not if said console is underpowered, because then its not gonna sell at all in the western markets.

Some Western 3rd party games can sell well on Nintendo platforms (Just Dance). However, it's very unlikely that Western games will ever sell as well as Japanese games in general.

Wait 3 days.

Put depends, but likely answer is no.
There is basically no evidence out there that makes me believe that 3rd paty games will not be gimped in one way or another on the Nintendo console. And no, I'm not talking the pathetic graphics war that is seen on ps4/one, comparing 900p to 1080p or some dumb crap.
Nintendo usually gets shafted by gimped features, announcement of no dlc, no online, late release, horrible fps/bugs or other things besides missing a few pixels.
You know factors that actually matter in regards to a game.

Easier said that done

They do everywhere else.

Bullshit, there are plenty of amazing Western 3rd party titles that equal or even surpass Nintendo games in quality. It's not the fault of Western publishers that Nintendo made so many stupid decisions with their hardware department that they've basically locked themselves out of the console business they created. 

The GTA games are terrific. The NBA 2K games are fantastic, anyone who knows anything about basketball knows that's a damn good representation of those games. The Witcher, Fallout, Destiny, FIFA, Madden, Star Wars Battlefront, etc. etc. are all good games. If you're going to say all those games are bad, then most of Nintendo's games fall into the same categorey (the Star Fox 0s, Mario Tennis, Yoshi's Wooly World, Kirby, etc.), as not every game Nintendo makes is a Mario 64 type title, not even close. 

Even on the NES and SNES when Nintendo actually was somebody in the console business many of the best games were third party titles. Plain and simple. 

Nintendo is among the best developers on the planet, but this idea that only they know how to make a good game is ridiculously asinine. They never have been *that* much better than the other top developers. 

There are far more quality games on the PS3/360 than there were on the Wii or Wii U. One developer/publisher can never stack up directly to like 30-40 developers, Nintendo should know this better than anyone, it's a big part of the reason the NES destroyed the Sega Master System, Sega's 1st party games on the SMS were great, it's not as if Nintendo's games were 10x better. It's all the overwhelming third party suport the NES had over the SMS that made the difference.