The British have used Welsh both in WW2 and more recently in Bosnia.

u/nae_co on this sub last year mentioned the Japanese using an obscure dialect of Japanese.

The Chinese PLA used speakers of Wenzhounese, a notoriously difficult dialect of Wu Chinese, in the 1979 Sino-Vietnamese War (Naomi Cao, 2010, Constructing China's Jerusalem: Christians, Power and Place in Contemporary Wenzhou).

Egypt used Nubian speakers in the 1973 Yom Kippur War.

Dialects of Finnish were sometimes used as impromptu secret language or form of identification during the Second World War. Here (only in Finnish, sorry!) is one story about a ranger patrol who forgot the password needed for safe return, but wasn't shot because the rangers spoke a distinctive dialect and the sentries deduced (after a lengthy, shouted conversation) that Russians couldn't fake it.

Similar schemes were used occasionally elsewhere, but as far as I know, not as a planned measure like with the Navajo talkers. However, dialects of Finnish can be (and used to be even more) impenetrable even to a native speaker who doesn't speak the same dialect, let alone to someone who had learned the language as an adult.

I would expect that dialects and lingo were used in a similar impromptu fashion by other nationalities as well.