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Sample rate conversion systems (expansion or decimation) are time-varying operators. For your example system of decimation by $M$ : $$ y[n] = T\{x[n]\} = x[Mn] $$ you can easily see that results of shift in the input and output are not the same; i.e., $$ y_1[n] = T\{ x[n-d] \} = x[Mn - d] $$ and $$ y_d[n] = y[n-d] = x[M(n - d)] \neq y_1[n]$$


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