IPA: //əbˈdʒɛkʃənəbli//
KK: /əbˈdʒɛkʃənəbli/
In a way that is offensive or unacceptable.
The comments were objectionably rude and hurtful.
Objectionably → It is formed from "objection" (from Latin "obiectio", meaning a throwing against or opposition) and the suffix "-ably" (meaning in a manner that). The word "objectionably" means in a manner that expresses opposition or disapproval.
Think of expressing an 'opposition' ('objection') in a certain way ('-ably') — that's why objectionably means doing something in a way that is disapproved.