The three juristic leaders—Abu Hanifah, al-Shafi‘i, and Ahmad (in the view most commonly reported from him)—held that such testimony is to be accepted, for admissibility is the default rule. They also relied on the report recorded by Abu Dawud (2340) and al-Tirmidhi (691) from Ibn ‘Abbas: “A Bedouin came to the Prophet (peace and blessings be upon him) and said, ‘I have sighted the crescent.’ He asked, ‘Do you testify that there is no god but Allah?’ The man replied, ‘Yes.’ He then asked, ‘Do you testify that Muhammad is the Messenger of Allah?’ He replied, ‘Yes.’ The Prophet said, ‘Bilal, announce to the people that they are to fast tomorrow.’”
As for the hadith presently under discussion, they interpreted it as applying to a desert Arab whose uprightness has not been verified.
Sharh al-Muntaha states: “The testimony of a Bedouin is accepted against a villager; and the hadith ‘The testimony of a Bedouin is not admissible against a townsman’ concerns one whose probity among the desert folk is unknown.”
The weightier opinion, therefore, is to accept the testimony of any Bedouin whose integrity is established—whether it pertains to their own affairs or to those of sedentary people—for that is the original presumption so long as no impediment to testimony is present. Allah knows best.