Sure.
Stoicism deals with the relationship one has with emotional states and living in a virtuous accordance with the universe. For some Stoics, this involved understanding more strongly. The Logos, the underlying divine order, exists as a logical principle of reason that the Stoic sought to determine its nature. The Logos operates as a principle much like a theoretical law of physics. This universal reason was linked with the study of both rhetorical and dialectic forms of logic. Stoics also frequently employed propositional logic. But moreover, Stoicism did not concern itself tremendously with coercion, force, or the temporal future so much as it did with the here and now of one's immediate surroundings. "How are my actions in accordance with the environment that surrounds me?" There was even a certain amount of criticism towards force, as it sometimes tries to control what was deemed to be outside of one's control or to negatively interfere with well-being of another. Force also frequently stems from acting on our passions. Wealth was not criticized per se, but it was when it was pursued in excess or driven by strong passions of lust, greed, and power. And as can be seen through some of Stoicism's most renowned followers, Stoics are typically found among Si/Ne-valuing quadras.
I know their types partially through my own individual study of Socionics, Stoicism, and these individual philosophers. We have also had past discussions about most of these people to varying degrees on this forum. I am slightly puzzled as to why you are wondering why a Fi-base type would lend itself to an ethical philosophy dealing with the cultivation of moral virtue and rationality?
First of all, Stoicism does not really demand anything. It seeks to cultivate a mind unhampered by disruptive passions that would interfere with judgment. It strives for rational selection. But this does not remove the bias of the individual. (The Stanford link below, for example, does not mention anything about removing bias.) If anything, clearing the mind of passions, allows one to potentially act stronger on one's bias. It merely helps orient the mind towards rational choices. Many prominent Stoics retained their biases. It is hard, for example, to argue that Cato the Younger, Seneca the Younger, or Marcus Aurelius were freed of bias in their judgments.
For further reading, I would recommend the
Stanford Encyclopedia of Philosophy and Marcus Aurelius's Meditations.