how important is the frame to slide fit on a 1911? how critical is this to make a gun shoot very accurate?

For both your posts - get a copy of one of the Kuhnhausen 1911 books .
You also have to decide what you mean by 'accurate ' .Purely target ,hunting ,SD or carry ?

To add to what Mete said. Slide fit in one of many factors that will help you pistol shoot better. There are other factors involved and it is the combination of these that make a pistol a top shooter. But over all in general it is very important to the overall function, reliability, and accuracy of the pistol.

Kuhnhausen's books or a Pistolsmithing book will go into detail on the how and why of slide fit.

I installed a "group gripper" from Brownells.
It really improves accuracy but won't effect
reliability.

Depends upon your definition of 'accurate'. A 1911 can be tuned to deliver 1.5" groups or less @ 50 yds, but how many folks can take advantage of this level of accuracy?

Answer: maybe 1 in 1,000 or one tenth of one percent. IF they're very lucky.

Slide fit IMO is one of the least important areas for accuracy tuning, actually maybe THE least important. For accuracy I consider the barrel fit to be of primary importance and the sight picture to be second with the trigger pull third.

Any other 'tightening', while it WILL increase pure accuracy, will also decrease reliability.

With no more than a well-fitting barrel, good sights and a good trigger pull, it's quite easy for a good shooter to roll beer cans at 50 yds with every shot, standing offhand. IOW a head shot on a deer would be quite easy @ 30 yds or less, with no slide rail tightening at all. I've killed several this way.
Regards, Joe

I am of the opinion that the critical things that actually improve the accuracy of the 1911 are a well fitted barrel (match grade preferred), a well fitted barrel bushing, and a very good trigger. Of course good target sights. I feel a fitted slide really only improves the accuracy of your brain. Unless the slide/frame fit is extremely sloppy how would a good fit shrink those groups? Think about it, the slide holds the barrel and sight...it's the basis of what fires the cartridge. I feel the same way about the fit of the AR 15 receivers. I really feel the tighten the slide idea came from when someone shook their military 1911 and the whole pistol rattled...that is the slide and the frame, the barrel and the slide, etc.

Often in advertisements on match barrels it will be stated how much just the addition of such an item improves your groups.