Is it permissible to listen to the lessons of a Shaykh who follows the Ash'ari creed, while exercising caution regarding him in matters of 'Aqidah, or is it not permissible to listen to him at all?

The Ash'ari school is the closest of the theological schools to the school of the Salaf and the People of Hadith. There is no harm in benefiting from someone who belongs to it, if one knows the points of deviation they have, such as issues of Attributes (of Allah) and Predestination, and if one can guard against these errors. For it is not a condition for one from whom benefit is sought that he be infallible, otherwise it would be impossible to benefit from many of the scholars of the Ummah.