) I would not go out if it rained tomorrow. (Here, the verb in the main clause is past "would," so “Would” here is used in a (if) conditional statement which contains an element of probability and has nothing to do with past tense. I would say # 1 is more correct with “ will not”.
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Does it sound strange if I change the verb from "rains" to "rained"?No, not strange. That's the right thing to do.