There are those that use baby wipes on Shabbos, and those that do not. And then there are those that use only the thinner ones and not the thick ones. What is considered thin and what is considered thick?
Just two nights ago we brought a few brands of baby wipes to Rav Moshe Heinemann to answer the question. In order to test them, he took each wipe one at a time and tightly squeezed it in his palm. If liquid dripped onto the table, Rav Heinemann felt it would be assur on shabbos. (Pampers brand) If no liquid dripped out, then he said it was mutar for shabbos use. (Amazon brand?) It doesn't appear to be a question of thick vs. thin, rather sechita/squeezing the liquid out of the wipe.
For a more thorough discussion, see here as well as the conclusion that Rav Asher Weiss' heter in understanding "the liquid is primarily on the surface of the wipe rather than absorbed within it, and the wipe is actually made of special non-absorbsive material. Therefore, if used gently, one cannot say with any certainty that liquid will be squeezed from the wipe, and it remains a davar she’eino miskaven, which is permitted."