Is their any obligation of Aveilus for a relative who doesn’t keep any mitzvos and is not frum at all?
The Kitzur S.A. writes explicitly that those who have thrown the yoke of mitzvos from their necks are not mourned over.
Answer:
The Rema (Yoreh De’ah 340:5) writes (based on the Or Zaru’a) that even though we do not mourn for somebody who has left the “ways of the congregation,” we do mourn over his children, who strayed from the path through no fault of their own.
Therefore, based on the assumption that most not-frum people today don’t keep mitzvos out of ignorance and lack of education, and not out of a rebellious act of throwing the yoke of mitzvos off their neck, the general custom is to mourn over non-observant family members.
See Emes Le’Yaakov no. 345; Shevet Ha-Levi 3:166.
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