Yeah, autolysis usually tastes "meaty" to me, but supposedly the fatty acids that the yeast spill out into the beer resembles the molecular structure of soap .... or some BS like that.
I've never gotten soapy from autolysis either, but then I think significant autolysis off flavors in beer are really rare. I've left yeast on plates for a long time though, and they have never smelled soapy. Meaty or brothy is a better description, although in my case at least some of that is from the media.
Anyway, fatty acids can be involved in the formation of esters and aldehydes and such. Fatty acid salts are soap-like from a chemical standpoint, but they are also fairly insoluble so it doesn't seem likely to carry over to aroma.
I really think when people say "soapy" they mean "perfumey in a way that reminds me of scented soap", because plain soap has virtually no smell. I think it is linalool. It is used widely in soaps, perfumes, and cleaning products, is present in cilantro, coriander, and hops (and some people think they smell soapy), and is also present in yeast. If autolysis smells soapy to some people, I think it's probably the linalool or a related molecule. Different sensitivities to different forms of terpene alcohols could explain why some people find it offensive at certain levels that others find it wonderful.