[1] Based on mainly Ketzos Hashulchan 146 footnote 32

[2] M”B in name of Tiferes Yisrael, brought in Ketzos Hashulchan 127 footnote 13. Vetzaruch Iyun from his later ruling brought in footnote below. One must say that he retracted his ruling. See as well Daas Torah brought next.

[3] Daas Torah 326/26 brought in Minchas Yitzchak 7/20

[4] 146 footnote 32

[5] SSH”K 14 footnote 49, in name of RSZ”A and others.

[6] A) It’s a Melacha which is not needed for itself [Eino Tzarich Legufa] being that the source of the Memacheik prohibition is by smoothening the skin of an animal which benefits the skin. This is opposed to here where the smoothening of the soap does not benefit the soap but rather is done for the person to use the dissolved layer. B) Since the inevitable smoothening of the soap serves no benefit, as it makes no difference to oneself whether it is smooth or not, it is therefore allowed to be done even Rabbinically, as by Mimacheik if one has no intent to benefit the item from the smoothening than it is not considered a Melacha at all, similar to the ruling regarding pouring cold water into a plastic cup [brought in “The Laws of Cooking Halacha 1 Q&A there!] C) It is done in a way of its normal use, and just like we say regarding food prohibitions that when done in its way of eating it is allowed, the same applies by soap when used in the midst of bathing.

Vetzaruch Iyun based on this why we needed the Magen Avrahams explanation for why smearing saliva is permitted, as reasons a/b as well apply by saliva and thus it should be permitted without needing the Magen Avrahams explanation.