Chicago Community Kollel Parsha Encounters Oct 23, 2009 discusses the issues with bar soap.
The Rama (326:10) writes that it is forbidden to wash one's hands with
soap on Shabbos. Three reasons are given for this prohibition. The
Rama explains that using soap on Shabbos causes it to turn into
liquid, which is a violation of Nolad (creating a new entity).
This reason is not accepted by the Magen Avraham (brought in Mishna
Berura 326:30). He argues that the main purpose of soap is not to
serve as a liquid, and therefore, the prohibition of Nolad is not
relevant to soap.
A second reason for the prohibition, mentioned by the Mishna Berura
ibid., is that using soap is in violation of Mimarayach (smearing).
Many Poskim argue that this reason only applies to soap used in
previous generations, which was rough and needed to be smoothed. This
would not apply to bar soap used in modern times, which is quiet
smooth. (Some brands of bar soap have pointy edges; perhaps smoothing
those edges is in violation of Mimarayach. Additionally, if a bar of
soap remains in water for some time, it can become pasty and soft. If
one wipes off the soft part in order to smooth out the bar, he may
have violated the prohibition of Mimarayach.)
A third reason quoted by the Mishna Berura, is that soap may be so
abrasive that it will pull out hair on Shabbos. This reason, too, does
not apply to modern soap.
In conclusion, there is a universal custom to avoid using bar soap on
Shabbos. Although the rationale behind this custom may be unclear, we
dare not tamper with this custom (Mishna Berura 326:30, Aruch Hashulchan 326:11,
Shmiras Shabbos Khilchasa 14:16, Ben Ish Chai II Yisro 15, Kitzur
Hilchos Shabbos 32:4). However in extenuating circumstances one may
wash his hands using bar soap. It is preferable, however, to use the
soap under running water (Shmiras Shabbos Khilchasa 40:11).