Storing a value just copies its binary pattern into memory, so signness is irrelevant here. But one has to differentiate between signed and unsigned types when loading a value narrower than the register width, because the CPU needs to know that it should zero extend or sign extend the value to fill the register.
Besides, ARM uses two's complement, which means addition, subtraction and non-widening multiplication on two values don't care that the values are signed or unsigned because the result will be exactly the same. The same to all bitwise operations except right shift. For the basic operations, only widening multiplication, division, comparison for larger than/less than and right shift produce different result for signed, thus require a different instruction. You should read this answer for more information.
Further reading