I too always use interfacing and I do not find my completed T-shirt quilts stiff in any way. They are always soft. They are also heavy as all get out but they are soft.
Unlike many, I iron on my interfacing after I cut my shirts. So if you have already cut them out, it is not too late to add interfacing now. Just cut out your fusible interfacing the same size as your T-shirt blocks and iron them on. You may get a wee bit of stretching around the edges but that can easily be hidden in your seam allowances.