Regarding using bar soap on Shabbos the following has been asked and answered. Using a bar of soap on Shabbat
My questions are in regards to liquid soap. May one use liquid soap on Shabbos? Is there a difference if it is thick or watered down?
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Rabbi Ribiat discusses this in The 39 Melochos (in the corrected edition, Misrad Hasefer 2004), Section 3/C/b-3.
He says that most poskim (notably, ערוך השלחן שכ"ו י"א) rule that one is allowed to use liquid soap on Shabbos, because Memarayach (a toldah of Memachaik) does not apply to liquids.
However, some poskim (notably, אגרות משה שו"ח ח"א קי"ג) rule that one is not allowed to use liquid soap on Shabbos, because of the thick lather that results from using soap. Therefore, some people use diluted liquid soap on Shabbos.
Interestingly, in that תשובה, R' Moshe writes:
.לכן אין נוהגין בביתי היתר זה, וכן ראוי להחמיר
Therefore, in my house we do not use this היתר; and so people should be stringent.
About diluting the soap -- Rabbi Ribiat writes (ibid) that one is allowed to dilute it on Shabbos if it wasn't done before Shabbos. Another option is to put the soap on the hand, and then run water on it without rubbing, so that it will dilute by itself, and then rub it and use it after.