Why catalyst does not alter the entropy of a reaction?
TL;DR Catalysts by definition do not alter the magnitude of changes in thermodynamic properties that accompany conversion of reactants to products, they only alter the conversion (reaction) rates.
The reason a catalyst does not alter the entropy of a reaction is that this is one part of the definition of a catalyst! Ideally none of the changes in thermodynamic functions accompanying a reaction are altered by the catalyst. However, that is a circular and not very helpful argument. The fundamental reason is that catalysts are not consumed in chemical reactions. Since the products and reagents remain the same, it follows from Hess's law that catalysts do not contribute to thermodynamic changes associated with the reaction.  Only the rate with which reactants and products interconvert (kinetics) changes.
Catalysts alter the reaction rate by altering the rate of encounter of the reagents or products or by assisting in formation of new lower energy (more stable) reaction intermediates. A catalyst may be as simple as a material that increases the proximity of reagents by increasing their local concentration, without otherwise altering their reactivity (bond enthalpies). That can be the case in either enzymes or solid supports. However catalysts often also alter reactivity by weakening specific bonds. An example of a catalyst that provides both functions is platinum.