What is the ruling on following and retweeting the accounts of respected non-believers or those with doctrinal deviations if their tweets are beneficial? Is it permissible to publish beneficial clips regardless of the background of the speaker? And what is the criterion for dealing with these matters—is it the predominant benefit, and is it a condition that the account owner's methodology be 100% sound for following or publishing their content?

It is permissible to retweet beneficial tweets or share a useful clip, even if the account also posts other forbidden things, and there is no assistance in sin in doing so. As for following the account, it is permissible if the غالب (preponderance) is the posting of permissible material, and it is prohibited if the غالب (preponderance) is the posting of objectionable things. It is not obligatory to ensure the soundness of the account owner's methodology 100% for following or sharing, as the consideration is the غالب (preponderance) of the account's content and the tweet or clip being beneficial and free from Shariah prohibitions.