Can 32% hydrochloric acid be stored in a milk jug (HDPE)?
There is more than just material composition to container selection. Yes HDPE is compatible with hydrochloric acid, but you have to consider rigidity and failure probability. Think: would you want to store Concentrated Hydrochloric acid in a 2 mil bag? Probably not because the probability of puncture and resulting loss/cost from the spill would be sufficiently high. Though not as extreme your milk jug is along those lines as it is softer and less rigid as the original container.

There is also the issue of legal considerations. In the US I'm sure that milk jug would not meet the DOT requirements for transport, and OSHA prohibits using containers typically used for food as being used for chemical or waste storage.

That said for home use only, you will probably be okay to store it, certainly not recommended, but this is the real world. I would at least recommend that if you do use a milk jug, you at least use a basin that can hold all of the contents for secondary containment in case of a leak which milk jugs occasionally do  AND certainly label the contents.