Ubisoft, Square Enix, WB, Activision and a few others will be there if there is money to be made, however I dont think the likes of Rockstar, Bethesda or EA would bother even if NX is a success.

If the NX sells well, 3rd parties will definitely be eyeing that console to release more games

and if the NX is 3rd party friendly

Business is business. Nothing is irreparable.

As long as there is somewhere like Playstation/Xbox that let third parties sell big numbers, they will not go back to Nintendo. The last time third parties sold well on a Nintendo platform was during SNES when Capcom, Square and Enix managed to get on top 20 list of best selling games. Since then Nintendo hadware sells Nintendo software. A few exceptions like Monster Hunter and Yokai Watch on handhelds does not alter the fact that people that invest in Nintendo mostly are interested in Nintendo software.

Go to the VGChartz database and look at the 20 top sellers on Nintendo systems. All the time since NES and Gameboy the Nintendo games have a massive presence. This is not the case for Playstation and Xbox, where third parties sell better than platform exclusives. Sega used to have the same situation as Nintendo with their consoles, selling mostly Sega games.

Japanese third parties for sure. The hard ones to get in ride are Square Enix and Capcom, but they also happen to have the biggest IPs of them all. But I believe Nintendo could get them back on board for their next home console. Capcom knows where the $$$ is at, so Monster Hunter might stick around... But those other franchises would come in handy too.

I believe Square Enix are going to support NX at first, hopefully I'm right.

Bandai Namco and SEGA are sure to support the next system, they're the most balanced of them all. Bandai Namco also happens to publish A LOT OF GAMES. Yes, Tales may not be with Nintendo now but It could return. Imagine Tales, Ace Combat, Dragon Ball, Naruto, all on board with NX, that would be great!

Then we have TECMO KOEI, which somehow are still in the business with their niche games that nobody seems to buy. They could support the NX too.

Konami isn't coming back.

And those are the major Japanese third parties. In the West maybe Ubisoft could jump back, EA/Bethesda/Activion not even. Disney will stick around.

Only if there is guaranteed money to make. And without them, there is no guarantee.

Oh, Nintendo treated third parties poorly since the eighties! I think they got better during the Gamecube era but, by then, they had other options.

Yes only if Nintendo plays by their rules ...

They'll hardly care about competing with first party games as long as they can make some good money on their new hardware ...

3rd party developer feedback is extremely important so that means having tight relations between ISVs and outside developers ...

To fix the relations with third parties Nintendo should stop being Nintendo, with all that it entails, good and bad.

So the real question is: Should Nintendo loose its identity and become another Sony and Microsoft?. And frankly, I'm not sure anymore...

This is a business. And, either Nintendo makes the investment, on the behalf of 3rd parties, worthwhile or they just won't come.
Simply put, Nintendo's games aren't "core gamer" appealing. Just look at the type of games that sit at the top charts year over year and then compare them with Nintendo games.

But that's not all.
Nintendo's marketing is mostly focused at the young gamer. Actually, it seems that Nintendo's strategy is based around that market. And this is nothing new.

Nintendo needs to do more than give 3rd parties a PS4/XB1 clone; a Sony and MS PR equivalent. They need to make exclusive games that focus on the tastes of Sony and MS gamers.
That is will make the market buy NX and consequently, make 3rd parties believe that they truly have a market for their games on NX.