Is it permissible for a Muslim to say "thank you" to someone who says "may you have good health" after sneezing, and is it permissible for him to say "may you have good health" to a non-Muslim when they sneeze, or is that considered imitating the disbelievers?

Firstly: It is permissible to respond with "thank you" to a non-Muslim if he says "may you be healthy" (or "to your health") when one sneezes. This falls under the category of good treatment and responding with kind words, following the example of the Prophet, peace and blessings be upon him, and his noble interactions with non-Muslims.

Secondly: It is permissible to say "may you be healthy" to a non-Muslim if he sneezes, especially if refraining from doing so is considered unethical in their custom. The principle is the permissibility of supplicating for a non-combatant non-Muslim with worldly matters. This has been authentically reported from some Companions, such as supplicating for long life, abundance of wealth and children, bodily health, and guidance.

Thirdly: If a non-Muslim praises Allah after sneezing, he should be supplicated for by saying: "May Allah guide you and set your affairs aright," just as the Prophet, peace and blessings be upon him, used to do with the Jews.