Is "leave out to dry" an accepted variation of "hang out to dry"?
I think you were mixing and matching two different idioms
Leave you hanging is one idiom that now appears far more used than "hang out to dry" ... if ngram works that is.
https://books.google.com/ngrams/graph?content=leave+you+hanging%2C+hang+you+out+to+dry&year_start=1800&year_end=2000&corpus=15&smoothing=3&share=&direct_url=t1%3B%2Cleave%20you%20hanging%3B%2Cc0%3B.t1%3B%2Chang%20you%20out%20to%20dry%3B%2Cc0
Cambridge dictionary
leave someone hanging:
to keep someone waiting for your decision or answer:
I was left hanging, waiting for the college to tell me whether I got a scholarship or not.
Leaving someone hanging evokes more clinging to a liferope or a ledge to me...but perhaps it shared the same laundry root ? : )
It doesn't seem 'leave someone out to dry' is an acceptable variant of 'hang someone out to dry'. While the Google Ngram Viewer does not find any n-grams for the former version, it shows that the latter version of the idiom is in standard use.
A discussion about 'leave someone out to dry' can be seen on the WordReference.com