Can you wish happy birthday to blood relatives on the martyrdom of lady Fatima (as),who are not Shia but are Muslims? If i do not send a message to wish them it will result into a family issue. As it has in the past due to Arbaeen being on a family members birthday,I did not wish them, it has lead to a big issue. What should one do?

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This should be avoided, but if really necessary can be done but without taking part in any celebrations etc on the day of shadahat