Is it permissible to use disinfecting kitchen or bathroom cleansers such as Fantastic or other spray or liquid cleansers (not thick ones such as SoftScrub) on Shabbos and/or Yom Tov? (Please pardon me if the answer to this question already exists on your site -- I was not able to find it.)

It is permitted to use liquid cleansers on Shabbat and Yom Tov but not a bar of soap. It should be noted that one should be careful of the prohibition of Sechitah (squeezing out liquid). Therefore one should use for cleaning a brush or special products which are not spongy material but synthetic material with fibers that are not overcrowded. (These laws are detailed in Shemirat Shabbat Kehilchata Chapter 12).