This is what I've used and it doesn't feel stiff to me but it really helps keep the shirts from stretching if you make sure you put the tricot's stretch perpendicular to the T-shirt's stretch.

I would use a lightwieght fusible and fuse them to muslin squares. The problem with using nothing to stabilize them is that they are, for lack of a better word, unstable.
The stretch in the fabric will cause the threads in the stitching to break then the quilt will fall apart. I think you're going to have to use some type of stabilizer.

My quilting friend and I use French Fuse we get from Hancock's. I think JoAnns has something like it. Makes for the softest quilt; we have made quite a few of these.

I just knew you guys would be full of ideas and suggestions. Already see some ideas I like here!!

I like this idea! Maybe try some on some scraps and see what happens? :D:D:D

Take some t-shirt fabric and try a 1:1 solution of Sta-Flo liquid laundry starch and water on it. (I paint this on with a large wall-painting brush, toss in the dryer, then iron with steam.) You will be able to tell if it stiffens the t-shirt material enough. I think it will, but I haven't actually done it with t-shirt material so don't know for sure.

Another option is to use MistyFuse. Although this is a fusible, it is *extremely* light and will not add stiffness. You would need a Teflon or applique pressing sheet to do this, as it does not have a paper backing. Amazon has some reviews of MistyFuse.

I have used tricot fusible for some applications. It does add less stiffness than other fusibles, but also adds some weight and thickness to the fabric.

I would perhaps experiment on old t-shirts (maybe from the thrift shop?) with these techniques to find the best one.

I've made many T-Shirt quilts and use an iron on tricot on the back of the shirts. The tricot is so soft and you don't even know it's there. There is a stretch to this tricot so you lay it on the shirt with the stretch going the opposite direction from the stretch of the shirt. I have never had a hard or stiff quilt top doing it this way. Or you could use a serger to put the pcs together. Because they stitch so fast and have such a long foot for some reason it doesn't allow the shirts to stretch. I have never had a problem using either of the above ways. They always come out soft and cuddly.

I got a stabilizer at Walmart that made my T-shirts feel just like cotton. The quilt ended up being nice, soft and cuddly. It comes in a plastic bag and usually hangs in the back of the fabric isle.

My goodness, I have not heard the term Turkey Trac, can you explain, I have a T shirt quilt ready to start and had thought I would use the base and place shirt pieces random on the top, then quilt it, your idea seems more appealing...
I am using a knit camo backing so I have to decide how to keep that from stretching....thanks for your help...memepeggy

I have made several tee shirt quilts and read much of the experts advice about them before I started ----- the tricot iron on interfacing is perfect - stays soft and pliable. Do as Dakotamaid said above -- put the stretch of the tricot in the opposite direction of the stretch of the tee shirts.