I am a non-native English speaker. When I was writing an English essay, a question came up my mind. Which word is better "carefree parents" or "easy-going parents" when I want to compare with "strict parents"?
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If they are exactly the opposite of "strict", I would call them "liberal" or even "permissive" depending on the intended connotation.
When we use "permissive" there is usually a certain criticism implied.
In general, in my area of the United States, the word of choice seems to be lenient - per the linked definition, “1. agreeably tolerant; permissive; indulgent”.
A very lenient parenting style I only recently discovered has been labelled: Free-range parenting. So some might be called Free-range parents. Their children are commonly called Free-range children, and there are documentaries on YouTube about that particular social phenomenon.