Is it considered a sin or abandonment to refrain from greeting some girls, or to avoid greeting a girl who bothers me?

There is no sin upon one who refrains from initiating the greeting of peace (salam), but they have missed out on what is recommended. Sin falls upon one who fails to return the greeting of peace. Initiating the salam is a confirmed Sunnah, while returning it is obligatory. One who desires good should not miss the virtue of spreading salam merely due to an imagined harm. Therefore, it is advised to offer salam to all women, whether there is a prior acquaintance or not. Merely refraining from initiating salam is not among the forbidden abandonment (hajr). And if the forbidden abandonment is permissible in cases of harm, then refraining from offering salam to one from whom harm is feared is permissible, especially if there was no prior friendship or brotherhood.