Is the sister sinful for being angry with her sister who boycotts her and abuses her due to her political views, even though the offending sister does not try to reconcile?

Anger and resentment are not blameworthy in themselves, except for the words and actions that result from them, such as cutting off family ties and verbal abuse. Your sister describing you as being against religion is wrong. You must maintain ties with your sister, be gentle with her, and treat her kindly, for Allah Almighty says: "And not equal are the good deed and the bad. Repel [evil] with that which is better; then behold, he between whom and you was enmity [will become] as though he was a devoted friend. But none is granted it except those who are patient, and none is granted it except one having a great portion [of good]. And if there comes to you from Satan an evil suggestion, then seek refuge in Allah. Indeed, He is the All-Hearing, the All-Knowing" {Fussilat 34-36}.