What is the ruling on the one who says in their posts: "I will consider you a disbeliever if you do not write 'Alhamdulillah,'" or "I will consider you a Jew if you do not share this picture"?

It is not permissible to force people to write or publish certain things by threatening them with phrases such as "We consider you a disbeliever." If the one making the threat is sincere in his threat, then he has declared Muslims disbelievers for something that is not disbelief, and the warning in the Hadith applies to him: "Any man who says to his brother, 'O disbeliever,' then it has returned to one of them; if he was as he said, otherwise it returns to him." And if he is a liar, then it is also not permissible because lying is forbidden. So, the writer is either declaring Muslims disbelievers or lying about them. And whoever sees these phrases should advise the writer and forbid him from them.