Is a follower [of a madhhab] obligated to adhere to a specific madhhab in all rulings, or is it permissible for him to adopt the opinions of other madhahib when they differ, such as the ruling on eating forgetfully during a Ramadan day?

Scholars differ for multiple reasons, and each follows what their ijtihad (definition) led them to. The four Imams are luminaries of the Ummah, and there is no blame in following one of their schools of thought, provided there is no fanaticism and the school of thought is abandoned when it contradicts a well-established Sunnah (definition). It is permissible for someone who follows a particular school of thought to follow a school other than that of their Imam in matters of ijtihad, as long as they do not intend to cherry-pick concessions. The most preponderant opinion is that whoever eats or drinks forgetfully, their fast is valid, and no compensatory fast is required of them.