How should we understand non-Muslims coming for the pilgrimage to Karbala and showing respect to Imam Hussain (AS), despite their denial of Prophet Muhammad (PBUH) and his household in their own beliefs?
Allah is generous and the Prophet (S) was generous and did not turn away people who asked for assistance, regardless of their religion. It is natural that some people will come to the holy sites to pay respects or seek blessings, even if they are not Muslim.
It is good to respect their decision, as long as they are respectful to the sanctity of the holy sites and respect the rites that are carried out at these sites (e.g. they are not behaving like some tourists, acting inappropriately, or causing problems).