Is it incumbent upon a fiancée to sever ties with her maternal cousins to appease her fiancé, who rejects even mere courtesy towards them, especially given that she does not wish to annul the engagement or sever kinship ties?

Clarify to him that cutting off kinship ties is a sin that Sharia (definition) has warned against, and there is no reason to abandon your female cousins. And that you are still a non-mahram (definition) to him; it is not permissible for him to look at you or to be alone with you. Inform him that you will be obedient to him if he instructs you not to visit them after marriage, and in that case, there will be no sin upon you. It is advised that a man should not be obstinate in demanding the severance of ties between a woman and her female cousins unless there is demonstrable harm.