I am home visiting my older parents who are obviously very concerned about the current pandemic R”L. My father asked me if it is permissible to use liquid soap on Shabbos especially in light of the pandemic. I told him it might have to be diluted first. Is that correct? I am also wondering if it is permissible to use alcohol gel sanitizer.

There are different opinions among the poskim how liquid does the soap have to be so that when it comes in contact with water it's not considered "nolad" (changing its form). Accordingly, being that we are talking about health issues, especially regarding older people where it may really be dangerous, and its only a rabbinic-not a Torah- prohibition, than your father definitely should (!) rely on the lenient poskim (who most rabbis hold like anyway) who allow liquid soap (although, if you really want to, I imagine that mixing in a little water beforehand shouldn't dilute it too much, if you really want to take the stringent opinion). The alcohol gel sanitizer is no problem whatsoever, because you don't mix it with water so there's no worry about "changing its form". All the best!