Don't judge someone with your looks when you don't agree with them.
Do not dismiss someone when you don't agree with them.
この場合の否定しない=do not judge (察する)か dismiss (却下)を動詞として使えます。
自分のその時の器量=with your looks
でも特に "with your looks" の必要はありません。judge and dismiss の動詞は器量も含まれている言葉として使います。
相手の考えに共感できない時=when you don't agree with someone.