Saying "bless you" to non-Muslims is generally considered permissible within Islamic teachings.
While there may be varying opinions on the desirability of making supplications specifically for non-Muslims to be blessed (in terms of religious guidance or forgiveness), the act of saying "bless you" in the common, secular context is not inherently prohibited (haram). The referenced source indicates one scholar sanctioned the permissibility of supplication for non-believers, indicating that it isn't inherently forbidden.
The phrase "bless you," in its common usage after someone sneezes, is often considered a polite social custom signifying well-being rather than a specific religious blessing for salvation or faith. This distinction is important.
Therefore, unless your intent is to specifically supplicate for their religious salvation, the act of saying "bless you" as a common courtesy is widely regarded as acceptable.
