Is a Muslim sinful if he does not visit his relatives, though he wishes to, but extreme shyness prevents him from doing so? And if he is sinful, what should he do?

Shyness can be praiseworthy or blameworthy. The blameworthy kind is that which prevents one from performing good deeds, such as refraining from maintaining kinship ties under the pretext of shyness. This is not true shyness but rather embarrassment and weakness. Whoever experiences it must rid themselves of it and resist the whispers of Satan. As for the praiseworthy kind, it is that which compels one to avoid indecencies and prevents shortcomings in acts of obedience. The Prophet, peace and blessings be upon him, considered it one of the branches of faith. Allah Almighty has commanded piety and the maintenance of kinship ties in the Holy Quran, and the Prophet, peace and blessings be upon him, encouraged maintaining kinship ties in authentic hadiths.