Generally speaking, writing or referring about skin colour or skin tone is not good habit in civilized society. So just for the sake of pointing out certain scientific factors, I would answer this question.
Kerala is diveded as North Kerala, Middle Kerala and South Kerala. It is respectively referred in old time as Malabar, Kochi and Travencore.Nevertheless at ancient times whole Kerala was called Malabar, with which Arabian and Chinese traders had trade relationships. Along with the ships of these traders different types of people like Arabs, Phoenicians, Moore, Armenians, Jews, Greeks, Romans, Chinese, Burmese, and European Colonialists ( Portuguese, Dutch, France and British) came to Malabar.
In North Malabar or rather North Kerala there were many mixing of different nationalities. Few settlements of Jews, Arabs, Kanay Christains and Chinese were also formed. They were permitted to build their worshipping centers like Synagogue, Mosque and Churches in the lands alloted by local Hindu Kings. These diplomacy was shown for good commerce and trade relations in spices. Some Kings encouraged people to embrace Islam or Christanity. Such people got very close to Arabian and Chinese traders, serving as translators, trade negotiators, stockists etc. Then marriages happened between the locals and fair skinned foreign traders. Many children of such marriages became fair skinned as per Indian standards. This is a general picture of that time when Kerala was very rich with spices exports.
It is a common belief that Nair and Thiya of North Kerala are fairer when compared to others. But there is no scientific evidence. It is also believed that beautiful Thiya girls were liked by British Colonialists and they had sexual relationship with them. Their children were fair skiined due to such partnership. But these girls were either slave types or had no voice in the family. Family head dictated everything .
Regarding Nair community the reason for their fairness have to be still studied. But not all Thiya or Nair people are fair. Where as lot of Muslims in Malabar and Christains in middle Kerala are fair. There are some ancient Christain families from middle east who settled in Kerala in 2 AD and they are very fair. Another Hindu community Ezhava has lot of people, who are fair skinned.
Where as majority of South Keralites are less fair skinned. It may be due to the less ancient trade activities and less interactions between different nationalities. Besides, South Kerala had no Thiya community and Nair community was diverse with respect to skin tone.
So we can not conclusively deduct that only Northern Nair and Thiya people are fair. There are Muslims and Ezavas very fair in North and Middle Kerala, and Christains in Middle Kerala.