If an innovator who has established a temporary marriage in his past, now declares it to be invalid and respects all the four Caliphs and our Prophet (Sallallahu Alaihi wa Sallam); is it permissible for a Sunni woman to marry him?

Praise be to Allah, the Lord of the Worlds; and may His blessings and peace be upon our Prophet Muhammad and upon all his Family and Companions.

If this man believes in false creeds that take a person out of the fold of Islam, then it is not permissible to marry him.  The ideologies that take the person out of the fold of Islam are:

The innovation of saying that the Qur'an is created, or neglecting the Attributes Allah, or saying that the companions of the Prophet (Sallallahu Alaihi wa Sallam) apostated after his death except a few of them, or saying that the Qur'an was distorted and things were taken out of it or added to it, or saying that the Walis (pious people) know what had happened and what will happen in the future, or know when and where they will die, or insulting Abu Bakr and Aisha (Radiya Allahu Anhuma) while the Qur'an praised them, or saying that Allah is everywhere in His creation.

If he does not believe in these Kufr ideologies but has dissolute innovations, and actions, then he is still not suitable for a religious, chaste woman, and such a woman should not marry him.

However, if a woman marries him, then there is a difference of opinion whether that marriage is valid or not.

Some of the people of knowledge are of the view that this marriage is invalid and some others said that it is valid but it is disliked.

Sheikh Al-Islam Zakaria al-Ansari said in Fathh al-Wahab: 'A dissolute person is not suitable for a chaste woman.'  It is a chaste man that is suitable for a chaste woman even if he is less known as being righteous than she.  An innovator is by no means suitable for a Sunni woman.'

However, if this person does not believe in Kufr or dissolute ideologies there is no harm in marrying him.

Our advice is the one of the Prophet (Sallallahu Alaihi wa Sallam), in the Hadith reported by Tirmizi and others, that Abu Hurairah narrated that the Prophet (Sallallahu Alaihi wa Sallam) said: "If a man whom you are pleased with his religion and moral qualities proposes for marriage then marry him, otherwise temptations and great mischief will spread on Earth."

Allah knows best.