The tires on the Corvette C6 in the FIA GT Championship are P275/35ZR18 on the front, and P325/30ZR19 on the rear. 3.8 inches of sidewall is what I would consider a good sidewall. (I have a tire size calculator and tire application chart)
Its actualy higher than what you see on alot of riced up cars seen on the streets. (less than 3 inches of sidewall)

In the picture it looks to me like the tires almost the same, even if the GTRs in LFS have 4 inch sidewalls it's still good enough to keep sidewall flex within the proper range.

I was told by a tire dealer that the range that you will find most high performance tires in will be 3-4 inches of sidewall. If you go above, the tire may be too flexible, if you go below, it may be too stiff. If he's right or not I don't know, but my tire chart doesn't show any real high performance tires below or above that range, only stuff made to sell to ricers. (an example of something made to sell to ricers would be a 225/30R17, at 2.7 inches of sidewall) Ricers seem to think that the closer the rim is to the ground the faster the car will go.

doesnt the 30 in the sidewall markings mean 30mm sidewall?

No, it means the sidewall is 30% of the nominal tread width

Quote from Stone in Focus :

doesnt the 30 in the sidewall markings mean 30mm sidewall?

As Tristan said, that´s a percentage, not a metrical measurement.
That means a tire with 30 has not necessarily less sidewall than a tire with 45 for example.

I'm fairly sure I recall a conversation during the commentary last season, where Martin Brundell mentioned that the tyre sidewalls are so large in F1 in comarison to most other motorsports, because the tyres are an integral part of the suspension.
The teams use the ability of the tyres to absorb the bumps in the road to enable them to keep the weight of the rest of the suspension system down.

Quote from Jamexing :

The only reason F-1 is sticking to tiny 13 inch wheels and high sidewalls is the rules that mandate them. If more sensible sizes such as 15 inch wheels and same overall tire dimensions were permitted, the current wheels will soon go the way of the dodo.

F1 cars (and some other serious single seaters) have very high profile tyres because most of the damping is done by the tyre, which allows very stiff suspension and chassis.

Correction: Most of the springing is done with the tyre (which is underdamped). It also isn't as true these days - watch F1 onboard and you can see the wishbones move. Back in the full ground effect era the tyre was pretty much the only springing medium, but not any more.

It apears to me that F1 has gone full circle in that respect, in the 60s the suspension did most of the work, then later on it was the tires that acted as most of the spring, now they are heading back to the suspension.

I realy don't think F1 will ever go to low(er) profile tires, the design of the cars would have to change alot, I don't think they are going to go that route.
F1 tires are so well engineered and established it would be pointless to change the design and have to start from scratch. It's not like they could just bolt on a set from a GT car and go.

Quote from ajp71 :

F1 cars (and some other serious single seaters) have very high profile tyres because most of the damping is done by the tyre, which allows very stiff suspension and chassis.

A little advice:

Go home and bounce a real tire (you can use ANY tire, from M/Ts to Race tires or even your car's spare tire). All you need to do is to position the tire absolutely straight (camber = 0 degrees). Use your hand to keep it standing if it's too high and narrow. Now, lift it up a reasonable distance (e.g. 50mm) and observe how it bounces.

And I'm generally treated like the ignorant fool around here...

As Jeremy Clarkson loves to say: "This is simply ASTONISHING!"

You might care to notice that it was almost certainly a mistake - he probably MEANT springing, but typed damping whilst distracted or something. Had you noticed that; had you noticed that I'd corrected him already; and had you noticed it was 2 days ago you might avoid the 'fool' label.