What are the matters of creed in which ijtihad and disagreement are permissible, and is the disagreement of the Ash'aris with Ahl al-Sunnah considered a legitimate disagreement and a valid ijtihad?

The issues of creed in which ijtihad and اختلاف (disagreement) are permissible are those that meet the criteria of permissible disagreement, where each proponent holds onto an evidence they deem superior and has not contradicted a text or a previous consensus. Such issues are very few. An example of this is the Prophet's (peace be upon him) vision of his Lord on the night of Al-Mi'raj.

As for the issues disagreed upon between the People of the Sunnah and the Ash'aris, they are not of this type of permissible disagreement, even though the Ash'aris are the closest of theologists to the methodology of the People of the Sunnah and Hadith.