How can one get rid of the hesitation related to not completely disbelieving soothsayers, a hesitation that arises from the apparent truthfulness of some of their statements due to jinn and devils supplying them with information, knowing that believing them—even conjecturally—is considered disbelief or a grave sin?

What soothsayers tell is of little truth and much falsehood. What they say truthfully is a word snatched by a jinn from the heavens, to which they then add a hundred lies. Scholars have forbidden believing these soothsayers and have considered anyone who believes them to be a disbeliever, outside the fold of Islam, because knowledge of the unseen belongs to Allah alone. The Prophet (peace and blessings be upon him) warned that whoever goes to a diviner or soothsayer and believes them, their prayer will not be accepted for forty days, and they will have disbelieved in what was revealed to Muhammad (peace and blessings be upon him).

Therefore, as long as you do not go to them or like hearing their news, you are upon goodness, and do not pay attention to whispers.