Obeying adverbs are provided in this article. The words listed here are commonly found along with the verb obeying in sentences. This reference page helps answer the question what are some adverbs that describe or modify the verb OBEYING.
blindly
implicitly
merely
simply
strictly
Hope this word list had the obeying adverb you were looking for. In addition to adverbs used with obeying, other example verb adverb pairings can be found on this site.
You can help by adding more adverbs in the comments. Thanks.