In British English, the noun Corbynista has been a disparaging appellation for a supporter of the British politician Jeremy Corbyn (born 1949), Leader of the Labour Party and Leader of the Opposition from Saturday 12^th September 2015 to Saturday 4^th April 2020. Jeremy Corbyn is a member of the left wing of the Labour Party.

The noun Corbynista is from:
– the surname Corbyn;
– the suffix -ista, after nouns such as Sandinista¹ and Senderista².
—Cf. also Guardianista.

¹ The noun Sandinista designates a supporter of the Nicaraguan nationalist leader Augusto César Sandino (1893-1934), and a member of the revolutionary Nicaraguan guerrilla organisation founded by him or of a similar organisation founded in his name in 1963.
² The noun Senderista designates a member of the revolutionary Peruvian guerrilla organisation Sendero Luminoso (i.e., Shining Path).

The choice of the suffix -ista to form the disparaging term Corbynista, therefore, was intended to liken Jeremy Corbyn’s supporters at best to radical socialists, and at worst to fanatics.

This reflected the moral panic that arose—not so much among the Conservative Party and Conservative media as among the right-wing trend in the Labour Party and Labour media ³—when Jeremy Corbyn became the frontrunner in the 2015 Labour Party leadership election.

³ Cf. Dump the Guardian!, a website showing how The Guardian (London and Manchester, England), a mouthpiece for the right wing of the Labour Party, relentlessly attacked Jeremy Corbyn from 2015 to 2017.

The text containing the earliest occurrence of the noun Corbynista that I have found reveals that moral panic; it is Nothing to lose but your fears, by Jane Merrick, political editor, published in The Independent (London, England) of Sunday 16^th August 2015:

In the shock and awe campaign to stop Jeremy Corbyn becoming leader, the weaponry of Tony Blair, Alastair Campbell and, this weekend, Gordon Brown has been discharged, with apocalyptic warnings that Labour is heading towards a precipice if the left-winger wins.
[…]
In the Labour leadership, is Corbyn a grotesque mediocrity, the next left-winger on the cab rank whose popularity is merely the result of circumstances, namely the anti-austerity movement in Greece and a leftist grassroots jolted back into life by a Conservative majority government? Or is he a genuine hero who, regardless of what happens on 12 September, has changed the party forever?
[…]
[…] Although it doesn’t seem like it to the Labour establishment, something extraordinary and, yes, wonderful has happened to the party in the past week. At the general election, there were just over 200,000 full members; now there are 245 short of 300,000. There are now 189,703 affiliated supporters and a further 121,295 registered supporters. In the final 24 hours before the deadline, 160,000 people signed up to vote for a leader. The total electorate is 610,753. These numbers are extraordinary, a democratic uplift of which Labour should be proud, not fearful.
It cannot be the case that all the new supporters and members are reds under the bed. Many of them are simply people who care about a vibrant opposition party. […]
[…]
The creation by Chuka Umunna and Tristram Hunt of Labour for the Common Good, which seeks to bring together soft left, old right, Brownites and Blairites, has happened only because of the Corbyn surge. If it works, there has not been this sort of unity in Labour for years.
And, curiously, if Corbyn gives Tom Watson, who is on course to become deputy leader, a job of party management, then the Blairites can stop worrying. As Blair’s former aide John McTernan wrote last week, Watson will save the party from any Corbynista takeover of the grassroots.
In the end, it is likely that Corbyn will not last the full term ⁴. He will either stand down or be ousted because he will be unable to whip his MPs through the opposition lobby, or, to misquote Marx […], he will self-destruct under his own internal contradictions. There is nothing to fear. Labour moderates have to learn to stop worrying and love the contest.

⁴ Unfortunately for Jane Merrick, Jeremy Corbyn was re-elected as Leader of the Labour Party on Saturday 24^th September 2016.