A very viral hadith is circulating nowadays stating: 

“Whoever offers congratulations to people for this blessed month, the Fire will be forbidden to him.”
The question is how sound is this hadith?

Well, we have not found any source for this hadith and it is clearly fabricated. Hence as a believer, we must not circulate it and be a part of spreading lies. It is not in any case permissible to attribute anything to Prophet Muhammad(peace be upon him) because such things come under the heading of telling lies against our beloved 

Prophet. And doing so is haraam and a major sin.
The Messenger of Allah (blessings and peace of Allah be upon him) said: “Whoever narrates a hadith from me knowing that it is false is one of the liars.”

Narrated by Muslim in the Introduction to as-Saheeh (1/7).
An-Nawawi (may Allah have mercy on him) said:
This is a stern warning against lying, which it indicates that whoever thinks it most likely that what he is narrating is false but still narrates it is a liar. How can he not be a liar, when he is narrating something that did not happen?
End quote from Sharh Saheeh Muslim (1/65)

Whatever is mentioned in this (so-called) hadith about hell being haraam for just a greeting is fabricated and comes under reckless talk. It is exaggerated which is an indication of it being false. Ibn al-Qayyim (may Allah have mercy on him) said: Fabricated hadiths sound strange, are poorly-worded and contain exaggeration, which clearly indicates that they are fabricated and are lies told against the Messenger of Allah (blessings and peace of Allah be upon him). al-Manaar al-Muneef (p. 50)

May Allah protect us all. As a believer, we must find the source of hadith and refrain from sharing such unauthentic sayings. It may sound good but not all good things are true.

May Allah enlighten us.