The used phrase seems to be have been patched together on the fly. While eine Abfuhr erteilen is frequently used, the combination Ablehnung erteilen sound strange. Erteilen frequently suggests an official statement, which does not seem appropriate for a disagreement (no matter, how intense).
I agree, that an interest group can only voice its opinion and desires, but hardly issue an official decision.
DWDS (see section "Typische Verbindungen") lists auf Ablehnung stoßen as one of the most frequent combinations.
I guess, that in the given examples it is simply sloppy phrasing (as opposed to an established technical phrase): a person has to accept (Zustimmung erteilen), while a proposal would be rejected (auf Abstimmung stoßen). This would require more complicated phrasing, so I consider the examples (acceptance or rejection of browser cookies, acceptance or rejection of vaccination) as preference of a slightly ugly use of verb (so it can be shared) to cleaner phrasing.
(Abfuhr erteilen would share the verb more easily, but has a somewhat rough connotation.)
Of course, plenty of alternatives exist, like
Zustimmung erteilen oder verweigern or even simpler: zustimmen oder ablehnen