Drunken Andrew Littlefair, 50, called Islam a "disgusting disease" and said mosques should be burned down and Muslims should be wiped out in a series of posts over four hours.
The father-of-one said in one, published on the morning after the Borough Bridge attack in London: "Give me bullets for my gun, I will shoot every b****** one."
He also said: "My granddad didn't fight and die for this."
Another read: "Go to the extreme and kill them all. Fire with fire."
When someone complained about the messages which were free for anyone to read, he did not remove the posts, so she called the police.
Teesside Crown Court heard that did not prevent him from posting on a new account a false apology for being a "white Christian who has values for life".
He added: "My views on this will nvr change sorry I am not!!!!"
Robert Mochrie, defending, described Littlefair as a "keyboard warrior" and said: "He doesn't have the intelligence frankly to be able to express himself in a more careful way."
He said the posts were "nothing more than utter stupidity, mumbling nonsense".
However, Judge Simon Bourne-Arton QC disagreed, saying they were the racist postings of a vile individual.
He said the posts followed the two terror atrocities in Manchester and London which had caused outrage.
"They went to the very heart of our democracy, they were appalling events and of course they resulted in a lot of ill-feeling towards certain sections of society and a lot of emotion.
"It was a time for people to be calm in the truest traditions of this country, it did not require people like you to stir up racial hatred."
Littlefair, of Trefoil Court, Norton, Teesside, admitted six offences of publishing threats to stir up racial hatred.
He smiled sadly to his daughter who was in the public gallery as he was led away.
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