There are differences in conventions and philosophy in different subjects. Mathematically, there are two natural symmetric monoidal structures on the monoidal category of graded modules over a commutative ring under the tensor product. In algebraic topology, the natural one is the one with signs. In algebraic geometry it is (usually) the one without signs. There is another related difference. Algebraic geometers allow sums of elements of different degrees and talk of homogeneous elements for contrast. Algebraic topologists generally think of graded modules as sequences of modules and do not allow the addition of elements of different degrees. The symmetry with signs makes little sense when elements are not restricted to be homogeneous.
To test whether you are an algebraic geometer or an algebraic topologist, ask yourself whether or not the Laurent series ring $F[x,x^{-1}]$ is a field, where $F$ is a field and $x$ has degree $2$, say (so this has nothing to do with signs). I once taught a joint course with a very fine algebraic geometer (Spencer Bloch no less) and we disagreed about the answer.
As to your actual question, signs are unlikely to appear out of the air when passing to associated graded rings. There is no reason why they should.
