Non,
Nothing special about the petrol used, just whatever one could purchase from local filling station.
In both my European and American vintage laundry manuals authors are split about using gasoline or turpentine for wash day. Standard advice was one added amounts of the stuff to soapy wash water as part of the boil wash. About a teacup or less full per boiler. It was supposed to help with cleaning, remove/prevent lime scale scum, etc... However as noted yes, the stuff did give one's wash a pong that hung around because no amount of rinsing truly removed. That is why some were in the "no" camp.
When it came to "dry cleaning" or spot removing at home, that was another matter.
Naphtha, benzene, gasoline, and later trichloroethylene, were all recommended. Yes, by the early 1900's you had standard warnings about using out of doors/well ventilated areas with no open fires or anything that could produce a spark.... but still.
Air is sometimes naturally charged, such as before or after thunderstorm. Flicking a switch or otherwise causing a spark or flame can ignite vapors from petrol substances even when a distance away from actual working area. In the clip above the housewife leaves that jug of gasoline open the entire time she is "dry cleaning".
Benzene IIRC was worse because the fumes actually move along the ground/floor and can travel some distance.
All this doesn't even touch the cancer causing properties of these substances. Benzene has no question about it; the stuff causes cancer which is why you don't see it on offer much in pure form as in days gone by. It is found in petrol fumes however and even tobacco smoke (cigars, cigarettes, etc...) which his a good reason to avoid "second hand smoke".
Some but not all of these risks were reduced or whatever when Mr. Fels came up with a way to bind Naptha to a soap, giving the world Fels Naptha-Soap. The rest as they say is history.
https://en.wikipedia.org/wiki/Fels-Naptha
https://books.google.com/books?id=1...UAhXCRyYKHYrgB-EQ6AEILDAC#v=onepage&q&f=false
In essence naptha soaps were the first petrol derived "detergents" in that the aromatic hydrocarbon bound to soap did away with much of the problems in using solvents in water. The addition of a solvent meant you got the powerful oil removing cleaner that worked without hard rubbing and even high temperatures.
Using any naptha soap in very hot to boiling water will cause the solvent portion to evaporate faster into the air. So you could use warm or even just "hot" water on wash day. Because the solvent was in the soap just rubbing the bar over a spot or stain often did the trick in terms of removal.