[drugstore]

Many great Hanafi Ulama especially between the 4th to the 7th centuries were Mu'tazili in aqidah.
Due to them being giants in the Hanafi madhab, their views are taken into consideration to a certain extent, however their views could only be adopted in issues that have no connection at all to their Mu'tazili beliefs.
That is why one would sometimes find Ulama adopting a view mentioned by a Mu'talizi Hanafi, then clarifying that the reason for this acceptance of his view is that this view couldn't be based on his Mu'tazili beliefs, thus it wouldn't matter here whether he is Mu'tazili or not.

This differentiating -between views that could be based on Mu'tazili though or not- isn't an easy task and is reserved for Ulama well-versed in aqidah as well as fiqh.
One will find examples of where an alim clearly mentioned that he adopted this view as it couldn't have anything to do with Mu'tazili aqidah, yet was later refuted by another who showed its connection to Mu'tazili belief.
This is why some prefer not adopting any views proposed by Mu'tazili's.

It should be remembered, that there is a huge difference between adopting the view of a Hanafi Mu'tazili and adopting the view of a non-Mu'tazili, that happened to reach us due to it being recorded by a Mu'tazili.
Mukhtar az-Zahidi, a famous Mu'tazili, has in his work "Qunyah" recorded thousands of Hanafi positions held by non-Mu'tazili giants prior to him. His book could be used, as long as the source isn't a mu'tazili.

As for Zamakhshari, one wouldn't find much fiqhi opinions of his in Hanafi works. He is generally relied upon for his mastery in the Arabic language or at times for views that he has narrated from earlier mashaikh or Imams of the Madhab. His beliefs wouldn't affect these issues.