The hadith is Sahih. It is recorded by Imam Muslim in his Sahih under the heading باب النهي عن ابتداء أهل الكتاب بالسلام (The prohibition of initiating the greeting with the People Of The Book).
The Prophet ﷺ said it to teach what is proper and improper behavior.
Initiating greeting (salam) to a disbeliever is at least makruh, although many consider it ...
Yes, this hadith is authentic. It is reported in Sahih Muslim
"Do not initiate greetings with the Jews and Christians. When you meet any of them in the road, then make him take its narrowest path." (Sahih Muslim 2167)
However, there is a context to it.
Ibn Al-Qayyim said,
"It is said that this was in a specific situation, when they were ...