Would a text written by a Rishi classified as Hindu scripture? If yes, are there any exceptions where a text written by a Rishi would not be considered as a Hindu scripture?
Yes.Surya is right. E.g., Brahmā Purāṇa is a work of Agastya ṛṣi(Rishi). That said, our ṛṣis are deemed authorities, meaning that if they asserted something (even without proof), it has weight which means their commandments are to be followed at all times.
Keep in mind that there are various hierarchies of ṛṣis and this information helps us to gauge their teachings' genuineness/importance → only ① Mahā & ② Brahma ṛṣis' say hold weight.