How much tire diameter difference?
 

How much difference between front and rear tire diameter can the ABS and traction control systems handle without freaking out? Mine are currently close to an inch different with no problems. Will 1.5" be more than the system can tolerate?

Or, can different front/rear tire diameters be programmed via HP Tuners or similar and keep those systems happy? Truck is 2011 Silverado 1500 2wd.

In a straight line, all 4 tires rotate at the 'same speed'. In a full-lock turn, the 'fastest' tire is the outer front and the 'slowest' is the inner rear.
Pretty sure that wheelbase, track widths, and max allowed steering angle all factor into figuring out the difference between
the inner rear vs the outer front during a full-lock turn;
Any difference larger than that - as a percentage - is very likely to activate one or more of those systems.
The lower the steering angle, the less difference the system wants to tolerate.

Don't know if HPTuner's or EFI LIve's 2011 GMT900 definition files - or even the speedo segments themselves in some as-yet undefined future -
have the ability to tolerate wildly different tire sizes.
Difference between 275/5R20 (31.91" tall) & 265/65R18 (31.56" tall) is ok,
but don't know if 275/5R20 (31.91" tall) vs 245/70R17 (30.50" tall) is enough to trigger false activations.
Note that the difference between 32" & 31" is less than the difference between 31" & 30", as a percentage;
they are NOT equivalent to the ABS / Traction Control / Stability Control Systems, even if we see them both as "1 inch".

Hmm... I hadn't considered the variable difference in tire speed during different circumstances such as full lock turn vs straight line, etc.

Thanks for your detailed thoughts on this, even though the question remains unanswered... I wonder where I can find out what the limits are?

Some cars come from the factory with different sizes front/rear, so obviously the factory can program the associated modules accordingly. But that doesn't necessarily mean it can be done at this point...

Where can you find out what the limits are? Anywhere you can perform a couple of full-lock turns. HOW can you find out?
Mark the inner rear tire with something that'll stain the ground, drive in a full-lock circle, measure that larger circle's diameter, THEN
mark the outer front tire with something that'll stain the ground, drive in a full-lock circle, measure that smaller circle's diameter.
Be thorough, do both left & right circles. (Suggested because I don't know how to do the math using steering lock degrees vs wheelbase vs track widths.)
Difference between smallest circle vs largest circle, as a percentage, is the tolerance LIMIT;
exceeding it will likely significantly increase false positive ABS / Traction Control / Stability Control activations.

It'd be pretty cool if the segment responsible for dealing with the speedo were either:
willing / able to accept differences between front & rear (if it only asks for the rear tire size, it expects that to be the front tire size as well
or
segment-swappable with a custom-written segment derived from a GMT900 pickup truck that could accept / account for different tire sizes.

Were I to take such a chance, I'd use slightly shorter front tires; if you use slightly larger rear tires, program for the larger rear tires. THAT IS A GUESS.

Hmm... interesting experiment. I think - correct me if I'm wrong - this would tell what the current difference is (doing it with current tires, that is) which we already know is tolerable to the systems. It wouldn't necessarily tell what the systems' tolerance limit is. One would need to do that with the proposed tire sizes to determine if those sizes are outside the tolerance limit. Or am I missing or misunderstanding something?

Yogi Berra might say, 'you won't know til you find out'; don't think you're misunderstanding anything.
Take small steps so you're more likely to approach the ABS Traction Controller's bullschidt threshold instead of stepping over it.

I think the way to do this is try to borrow - or find used and thus super cheap - front tires 1-1/2" shorter than the current back tires and run it. See what happens. Otherwise it's an expensive experiment with a fair amount of risk. There's a used tire place locally and a couple of body shops. Maybe I can get a spare pair or wheels, too, to make the swapping out for testing easier.