Crystallographic Information Files (CIF) are, in general, obtained from experimental measurements. Since the information originated from real samples, is it mandatory to relax the structure in order to determine "better" atoms positions and "better" cell parameters?
It depends somewhat on the properties you are interested in. Meaningful vibrational modes, for example, require that your geometry is an energy minimum for the method you are using. Since the experimental structure is unlikely to be energy minimum for an arbitrary electronic structure method, you should optimize starting from the experimental structure. Its also important to consider whether you can properly account for temperature effects computationally. This can be challenging for electronic structure techniques, but even classical dynamics can have issues. There can be disparities between the phase diagram of your computational approach and the experimental phase diagram.
On the other hand, for properties where it is not crucial to be at an energy minimum, it would likely produce better agreement with experiment to use the experimental geometry. For example, while methods to determine electronic absorption or linear/circular birefringence do require finding a stationary electronic state, these properties are still meaningful away from a nuclear minimum. Birefringence in particular is very sensitive to the electronic configuration and so its important that your simulation and experimental geometry match; otherwise, if there are errors, its difficult to determine whether they stem from deficiencies in the property calculation itself or from deviation between the geometries.
This is a very intriguing question.
I'll answer assuming that your CIF is formed by a molecule-based crystal. The structure in such CIF has been obtained usually by the X-ray diffraction technique. With it, you can obtain a single cell that, repeated in the 3 spatial directions, forms the total crystal structure.
Considering this, if you isolate just one molecule and perform the structural relaxation, you may obtain a structure that may be far from the original crystal. This makes the necessary standard procedure of obtaining the minimum energy structure invalid, for example, to obtain the vibration frequencies of the molecule in the crystal. In this work, Escalera-Moreno, explained the detailed procedure they followed to select the initial structure where the vibrations were calculated. I think it may be useful for you to take a look at it.