The question was asked if it is permissible to use soap on Shabbat, or would it be considered a transgression of the forbidden Melacha known as ‘MiMacheik’?
There is a lenient opinion, which is that of Rabbi Yitzchak Lampronti (1679-1756) as written in his sefer ‘Pachad Yitzchak’ that says bar soap is permissible on Shabbat. But, that is a single opinion. It is the consensus of most Acharonim including Chacham Ben Tzion, Rav Moshe Feinstein, and Chacham Ovadia Yoseph that it would be more preferable to use soft soap. Today, soft soap is especially easy to come by, and most people in fact already have soft soap in their homes.
There is one point about soft soap however, that must be noted. Chacham Ben Tzion makes it clear that the soft soap should be watered down. He holds that soft soap still has a little thickness to it, and the problem of ‘MiMacheik’ can still exist. ‘MiMacheik’ is the forbidden task on Shabbat of smoothing out or rubbing, which is the basis used by the consensus of Acharonim for restricting use of bar soap on Shabbat in the first place. Chacham Ben Tzion therefore says, it would be proper before Shabbat to prepare diluted soft soap by watering down the soap. This way the soap will not be thick at all but rather free flowing and thus permissible to use.
To review, those who are lenient to use bar soap on Shabbat should not be scolded as they have the Pachad Yitzchak to rely on, but the preferred method is to dilute soft soap in advance in order to avoid any problem.