The Judeo-Christian god does not exist, nor any other god, so I'm not sure what rights you're referring to. Are you referring to human rights? We don't need a religion to justify those.
Anyway, you said your argument accounts for it, but didn't actually follow through and demonstrate why that is. How does your argument take into account the aforementioned power imbalances?
God-given rights refers to a certain theory of rights that does not require theism.
It is a well and widely understood term whose usage should not invite “correction”.
Referring to God-given rights invokes their definition, which should make the inconsistency I was referring to clear.
Can you give a less vague answer?
No. Normally I would, but you are either being lazy or just plain acting in bad faith.
1. My answer is not vague. You are refusing to look up the critical definition. 2. Everything you have brought up (except for the theism bit, which is just completely off-topic) was preemptively addressed in my initial comment.