What is the jurisprudential criterion that determines when a prophetic command is binding, making its a ترك (omission) sinful, and when it is merely recommended, especially in matters for which there is no Quranic text, such as "Change gray hair but avoid black" and "Make marriage distant"?

The default rule for a Prophetic command, when devoid of any accompanying indicator (qarinah), is that it signifies obligation and bindingness, and whoever abandons it incurs sin. This is based on the Almighty's saying: "And let those who oppose His command beware, lest fitnah strike them or a painful punishment befall them," and His saying: "It is not for a believing man or a believing woman, when Allah and His Messenger have decided a matter, that they should have [any] option in their decision." If an indicator is found that diverts the command from obligation, it is then interpreted according to what that indicator signifies, whether it be recommendation or permissibility. There are other opinions held by some scholars, suggesting that the command indicates desirability (istihbab), or a more general request (talab al-a'amm), or distinguishing between the command of Allah and the command of the Messenger.

Regarding the Prophet's (peace be upon him) command concerning marriage, there is no original prohibition against marrying close relatives. As for the prohibition of anger, it has been said that its meaning is to avoid its causes, not anger itself. The Prophet's (peace be upon him) command to change gray hair is not for obligation, and his prohibition of black dye is not for prohibition according to some scholars.

In general, a command in the texts of revelation signifies obligation, and a prohibition signifies unlawfulness, unless there is evidence that diverts them from their original meaning. When in doubt, one should ask people of knowledge or refer to the commentaries on hadith (definition).