Bhishma, Vyasa and Satyavati nurtured him.
Was Satyavati uninterested in Vidura?
It is not mentioned in the Mahabharata that Satyavati was not interested in Vidura as he was a son of Dasi. Dasi's varna is not the reason for not mentioning the name. There's nothing wrong with the Dasi. It was Ambika's mistake that she didn't go to Vyasa for a child for the second time. It is against Shudra dharma to disobey their master or mistress. So, she acted according to her Dharma. There are many other instances (in Vedas, Puranas and also in Mahabharata itself) where even Brahmana's are also not mentioned. Who knows she was awarded by Satyavati because she has begotten a son who is well versed in the doctrines and an expert in war strategies. From chapter 106 of Adi Parva,
O king, the great Rishi of rigid vows, was well-pleased with her, and when he rose to go away, he addressed her and said, 'Amiable one, thou shalt no longer be a slave. Thy child also shall be greatly fortunate and virtuous, and the foremost of all intelligent men on earth!'
Considering Vyasa's words as true, her slavery was abolished after begetting Vidura.
Who raised Vidura?
The three children Dhritarashtra, Pandu and Vidura were mainly brought up by Bhishma but Satyavati and Vyasa also had role in raising them.
And Dhritarashtra and Pandu and Vidura of great intelligence were from their birth brought up by Bhishma, as if they were his own sons. And the children, having passed through the usual rites of their order, devoted themselves to vows and study. And they grew up into fine young men skilled in the Vedas and all athletic sports. And they became well-skilled in the practice of bow, in horsemanship, in encounters with mace, sword and shield, in the management of elephants in battle, and in the science of morality. Well-read in history and the Puranas and various branches of learning, and acquainted with the truths of the Vedas and their branches they acquired knowledge, which was versatile and deep. And Pandu, possessed of great prowess, excelled all men in archery while Dhritarashtra excelled all in personal strength, while in the three worlds there was no one equal to Vidura in devotion to virtue and in the knowledge of the dictates of morality. And beholding the restoration of the extinct line of Santanu, the saying became current in all countries that among mothers of heroes, the daughters of the king of Kasi were the first; that among countries Kurujangala was the first; that among virtuous men, Vidura was the first; that among cities Hastinapura was the first. Pandu became king, for Dhritarashtra, owing to the blindness, and Vidura, for his birth by a Sudra woman, did not obtain the kingdom. One day Bhishma, the foremost of those acquainted with the duties of a statesman and dictates of morality, properly addressing Vidura conversant with the truth of religion and virtue, said as follows."
From the above passage, it's clear that Vidura received respect in the country due to his virtue and knowledge. Vyasa and Satyavati also raised Vidura along with the other two.
Bhishma said, 'This our celebrated race, resplendent with every virtue and accomplishment, hath all along sovereignty over all other monarchs on earth. Its glory maintained and itself perpetuated by many virtuous and illustrious monarchs of old, the illustrious Krishna (Dwaipayana) and Satyavati and myself have raised you (three) up, in order that it may not be extinct.
He was later married to the daughter of King Devaka begotten a Sudra woman.
"Meanwhile the son of the ocean-going Ganga heard that king Devaka had a daughter endued with youth and beauty and begotten upon a Sudra wife. Bringing her from her father's abode, Bhishma married her to Vidura of great wisdom. And Vidura begot upon her many children like unto himself in accomplishments.'"
Because Vidura was also born through Niyoga just like Dhritarashtra and Pandu. Satyavati, Bhishma and Vyasa never shown a difference because he was a Shudra. Bhishma raised the three like his own children without any bias. He made Vidura as the minister of Hastinapura because he was well versed in doctrines of morality.