Is it necessary to take into account in practice the influence of refraction on the measured angular distance between the components

Is it necessary to take into account in practice the influence of refraction on the measured angular distance between the components of a binary star with a distance of the order of 1 “and why?

No, because for them the difference in refraction is vanishingly small.

Remember: The process of learning a person lasts a lifetime. The value of the same knowledge for different people may be different, it is determined by their individual characteristics and needs. Therefore, knowledge is always needed at any age and position.