From what I understand by "complacent acceptance", is that, someone accepts something without a doubt or without any cross questioning.
Is my understanding correct or is there more to it?
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You are almost exactly right about the meaning of complacent - which is used in a broad range of contexts with very similar effect. Typically the meaning is that the "complacent" person has assumed something - usually, something to their comfort or advantage - without examining the details of the situation. For example:
The factory owner had been complacent about the safety of his processes.
The politician complacently expected that she would be re-elected in the coming vote.
You don't give any context for the phrase "complacent acceptance", but the meaning is the same - assume things are OK, without checking. One of my friends regretted his complacent acceptance of a job contract, because the promised pay rise was not there in writing!
It seems to be a "nonce" expression. It has been used only once, in the title of a The Complacent Acceptance of Diversity: Human Resource Development in a Culturally Diverse Environment about the inability of work organizations to achieve racial balance.