The testimony of those who differ in madhhab, some of them regarding others

The answer – and Allah is the One who grants success – is that it is appropriate that the testimony of some followers of madhhabs against others who are not upon their madhhab not be accepted; because of what usually arises between them of enmity. And it has been established in the Sacred Law that the testimony of an enemy against his enemy is not accepted. This is in addition to the fact that each party sees the other as not just, so that each of them may then impugn the witness as being unjust.
As for the testimony of the Mujbira (Jabrites), for example, some of them for others, or the Mushabbiha, or the Murjiʾa, or any adherents of a madhhab when some of them testify for others in front of a judge – then that judge may rule on the basis of that testimony, even if he does not regard the people giving testimony as just according to his own madhhab.
The proof of that is the ruling of the Prophet (May Allah bless him and his family and grant them peace) by stoning the two adulterous Jews after he came to Madinah, based upon the testimony of some of the Jews that they had committed fornication.
In this case, it is required that the witnesses be acceptable to the people of that group.
Branching from this is the acceptance of the testimony of the Bedouins, some of them for others, in matters of sales, marriage, divorce, and the like; and similar to them are many of the people of remote regions who are far from Islamic teachings, and many of the people of villages whom ignorance has overwhelmed. The testimony of some of them for others is accepted by analogy with what has preceded, provided the witnesses are among those whose testimony is acceptable in those lands.
What has compelled us to what we have said is necessity. Allah, Exalted, has permitted the testimony of non-Muslims in cases of necessity, in His saying: “O you who have believed, testimony between you when death approaches one of you at the time of bequest is (that it be) two just men from among you or two others from outside of you, if you are travelling through the land and the disaster of death should strike you” [al-Māʾidah:106]. If the testimony of those we have mentioned were not accepted, contracts of sale, marriages, and all other contracts would be invalidated, and from that there would follow a great amount of corruption, and we would open upon people a door of tremendous evil. Allah, Exalted, says: “Allah intends for you ease and does not intend for you hardship” [al-Baqarah:185], and He says: “He has not placed upon you in the religion any difficulty” [al-Ḥajj:78].

Source: Min Thimār al-ʿIlm wa al-Ḥikmah vol.2