I doubt it would be a problem for the microbiome [1] but I would worry about the immune system. Would being inside in sterilized air all the time mean you can't go outside or into a forest without getting really sick?

[1] but who am I, it would still be worthwhile to check obviously

The underlying thought is that outside air (such as a forest) gets UV sterilized by the sun. So this would bring inside air up to the sterilization level of outside air.