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Do you mean that filter phase will not remain linear?
As far as I know in real implementation it is important for the filter's phase to be linear.
As you know the conversion between ideal filter and the casual one is nothing special in real practice. Just some delay elements.
Real filters have also linear phase.
Real filters are approximations to the ideal "brickwall" filter. It is possible to obtain exact phase linearity (but not "brickwall" amplitude response) with an FIR digital filter. All you need to do is make sure that the filter coefficients (multipliers) are symmetrical with respect to the middle coefficient. The well-know "moving- average" filter is one example.
You can obtain neither exact phase linearity nor brickwall amplitude response with an analog filter. There are several filter types that provide various degrees of phase linearity. The Bessel filter provides reasonable phase linearity over a wide frequency range, but its amplitude response is lousy. Another approximation to an analog linear phase filter is the "equi-ripple" phase response filter. Filter coefficients for these filters are available in the published literature.