May one perform Meleches Ochel Nefesh on behalf of a non-religious Jew?

A Jew who is a Mumar or desecrates Shabbos in public has the status of a gentile with regards to all matters.[1] It is thus forbidden to perform Meleches Ochel Nefesh on behalf of such Jews on Yom Tov.[2] [See Chapter 5 Halacha 5 regarding non-religious guests!] Some Poskim[3] however rule it is permitted to perform Melaches Ochel Nefesh on behalf of any Jew. This especially applies if the Jew is a Tinok Shenishba.[4]

Karaits:[5] Some Poskim[6] rule it is forbidden to perform Melached Ochel Nefesh on behalf of a Karait. Other Poskim[7] rule it is permitted to perform Melacha for a Karait.

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[1] Admur O.C. 39:1 “He is like a gentile for all matters”; Michaber Yoreh Deah 2:5 “He is like a gentile”; Admur Y.D. 2:10 “He is a like a gentile regarding Shechita and for the entire Torah, except for Kiddushin”; Rashba 7:53; Tiferes Lemoshe 113:9 [brought in Pischeiy teshuvah 113:1] regarding Bishul Akum [however not Pas Akum]; Erech Hashulchan 112:2; Kaf Hachaim 112:11; Ketzos Hashulchan 101:5 and Kitzur Shulchan Aruch 72: “Anyone who publicly desecrates Shabbos is considered like an idle worshiper and [thus] if he touches wine he forbids it, and the bread which he bakes is like Pas Akum, as well as the food which he cooks is like Bishul Akum.”

[2] Mabit 1:38 in name of Rabbeinu Shimshon; P”M 512 A”A 1 and M”Z 1; M”B 512:2; Kaf Hachaim 512:4

[3] Yearos Devash end of volume 1

[4] Maharam Shick 281 that so is opinion of Maharashach brought in M”A 512:1 regarding the Karaim; See P”M ibid

[5] See M”A 512:1; M”B 512:2; Kaf Hachaim 512:3

[6] Reb Betzalel 63 in name of Radbaz; 1^st opinion in M”A 512:1, Kneses Hagedola 512, Elya Raba 512:1, M”B 512:2

[7] Maharshach 3:15; 2^nd opinion in M”A 512:1, Kneses Hagedola 512, Elya Raba 512:1, P”M 512 A”A 1, M”B 512:2