Is it obligatory to abandon social media applications (such as Snapchat and Twitter) due to the presence of advertisements for companies or channels (like MBC) that have previously displayed content offensive to the religion, even if the advertisement itself does not contain mockery? And is it permissible to follow beneficial programs on MBC despite this?

Your benefiting from useful programs is permissible, and the appearance of permissible advertisements on them does not affect this, for there is no direct involvement in haram (definition) or assistance in it. The basic principle regarding things is permissibility unless there is a Shariah prohibition. And watching permissible content on channels is not blameworthy. One must be wary of obsessive whispers (waswas).