If it's not perfectly square, the countertop installation becomes seriously more difficult. And the backsplash, too.

Take the time to make them totally squared with each other, and totally levelled.

It makes the rest of things easier

i thought the countertop people would be able to accomodate for this when they do their templating. Is it difficult to cut non-square slabs of stone?

In most cases the countertop people can and will accommodate out of square walls. IF the wall is less than 90 and the counters go wall to wall then something needs to be done. I can't remember the last time we fixed an existing out of square wall, a couple of degrees is not at all uncommon.

It needs to be planned for in the design- provide a way to finish the ends to the wall-extended sides, fillers, scribe molding... (also applies to out of plumb). The type of corner cabinet being used is a factor and frameless are a bit fussier in this instance. Finally the installer has to work it out in layout.

Don't forget flooring--a lot of floor types will scream "crooked" if they don't have something square to line up with.

Weebbly-wobbly you get an award for just showing up isn't good enough for cabinetry installs. There are standards for a reason, not just to make an installer's life harder. If your installer cannot do a correct install, get someone else.

It occurs to me I should have asked how much out?

I was assuming typical construction- 1/2 degree or less-I spent a lot of time in a world where "perfectly square" was just that. I don't expect (and rarely see) it in buildings. I do expect not to see the problems when done though.

1/2 a degree needs a total of 7/8 compensation at the wall (faces of run are kept square so no floor problems btw). That would be 7/16 each leg. Bows and out of plumb change things- sometimes better, sometimes worse.

Checking square in an existing kitchen is a challenge of it's own. It is useless to check the corner with a framing square due to mud build up. The walls need to be checked further out from the corner. There are a few ways but perhaps the easiest for most is with two triangles and a straight edge.

Image attached- triangles 15" from corner to avoid mud build up- this wall is out 1/2 degree which leads to a gap of 5/32 at one end of the straight edge.
Once you know what you are dealing with talk with installer-how do they want to handle it. Then design parts as needed. As I said earlier the counter is not usually an issue.

Jakuval - You're solution is overly complex. Measure out from the inside corner 3 feet on one wall and 4 feet on the other wall (or any multiple of those). If the corner is square, the distance between those two points will be exactly 5 feet. It's called the 3-4-5 rule. The longer you can make the 3-4 dimensions, the more accurately you can measure for square.

A simple 345 won't work with mud build up.

Place two triangles and a stick- is it square or not -simple. Guessing how thick the mud is gets complicated.

The 3-4-5, 6-8-10 etc... is the best, and in my book, the only way to check for squareness.
And as rmtdoug states, the the longer the distance, the better.

345 is great for rough framing. 1/8" off equals 1/2 degree.
Triangle is foolproof, don't have triangles, fold paper

345 is the best way to check walls for square; mud, schmud. Cabinets have to follow walls, square or not. Everything will be fine as long as the cabinets stay on plane to each other. Don't ever expect a top fabricator to bail out poor cabinet installation.

Jakuval - If you are concerned about mud thickness, use a spacer against the wall away from where there is mud and snap your lines from that. Where they intersect at the corner is your starting point. Make your measurements along those lines.

Using multiple triangles and making jigs just compounds errors. Simple is best when measuring. When doing large amounts of cabinets, lay out a level reference line around all walls and use a story stick from there. Much more accurate than tens or hundreds of tape measure readings.

Rmtdoug- I am not talking about doing lay out.
I was offering a home owner a way to check square in an existing kitchen where everything is still in place to determine what needs to be ordered.
No jig, items at hand, fast, easy and just like a story pole..
"Much more accurate than tens or hundreds of tape measure readings"

My understanding is that the OP is asking about laying out cabinets on walls possibly not at 90 degrees to each other. 3-4-5 uses the entire wall to check for squareness. What they find will determine how to proceed. The primary concern is getting the base cabinets at 90 degrees and perfectly level because of the counters and backsplash.

Your diagram uses two triangles, a straight edge, and the first couple feet of the wall. Unfortunately, that will not be as accurate as using the entire wall and multiples of 3-4-5. Nobody is saying your method is wrong but that it's the less accurate method for this particular application.

I agree that doing layout 345 is the way to go, once you can get at the actual wall at the bottom (no mud), have done it for decades

I took it differently-OP has a lot of threads going, it seemed like they are planning and had not yet ordered-which is why I said "existing kitchen" (where 345 is inadequate.)
it's basic. Know what is and isn't level, plumb and square before beginning design, and certainly before anything is ordered so it can be accommodated.

Maybe you're right and OP is doing layout sitting in a gutted kitchen trying to figure out what they need.

Measuring existing conditions with cabinets in place-345 is not sufficient.

Should you ever decide to give it a tumble-you can place triangles further over and get 3ft of wall with a 3ft straight edge- 15 is simply the minimum to clear mud and usually avoids another drywall seam.
Need a longer run of wall to make you happy-use your big level for a straight edge (and check the wall to avoid placing triangles over seams in the drywall). Fast, accurate, able to account for discrepancies in the wall surface.

"Cabinets have to follow walls, square or not."

Why?