Is emigration obligatory for one who cannot practice the apparent prophetic traditions (Sunan al-Hady al-Thāhir) in his country, knowing that his departure would affect the sectarian balance? And is it more preferable to endure and cooperate, or to emigrate to apply the Sunnah?

You are not obligated to emigrate from your country as long as it is a land of Islam. It is preferable not to emigrate due to the great benefits of your stay, such as spreading the Sunnah and increasing the number of people of truth, while adhering to outward guidance (hady dhahir) as much as possible. What you are unable to do of outward guidance, there is no sin in abandoning it, especially if abandoning it serves a religious interest or repels harm. Indeed, Shaykh al-Islam Ibn Taymiyyah permitted abandoning outward guidance or sharing it with disbelievers if it served a religious interest, such as da'wah (inviting to Islam) or repelling harm from Muslims.