If you follow Labour politics, you’ll have read many appeals in recent months for a crackdown on abusive and bullying behaviour by Corbynite activists towards their moderate peers. Jeremy Corbyn stands accused of opening the doors of the Labour Party to teeming thousands of misogynistic “brocialists”, racist anti-Israel zealots and bullying “Trots”, who are terrorising MPs and members into a state of silence. Corbyn, this argument goes, has done too little to root out this behaviour, and probably secretly approves of the manner in which it chills and suppresses his parliamentary critics.

Many on the Left find these accusations galling, and it’s easy to see why. The press is generally quick to raise the alarm over allegations of abuse, and nowhere to be seen when those accusations turn out to be somewhat questionable – or even, in some cases, to be fabrications. It is deeply regrettable, too, that some observers have blurred the lines between criminal malice and genuine democratic agitation, as when the Guardian columnist Suzanne Moore reflected on Twitter that “[the] level of abuse to anti -Corbyn people [concerning] Rape/ death/deselection [is] out of control”. But these genuine inequities in how the issue is reported and analysed do not mean that a problem does not exist. The party has more than doubled in size, and the number of people who feel deeply, personally invested in Labour’s internecine struggles has grown immeasurably; it was always inevitable, in these circumstances, that there would be a big increase in abusive and threatening discourse, as part of an enormous growth in discourse generally. The arrival on the scene of opportunistic trolls from every Internet hellhole has made matters worse.

But if we’re serious about tackling abuse, we have to acknowledge something else: verbal or even physical bullying is not a one-way street within Labour, and Corbynites have been falling victim to it as well as moderates. Indeed, perhaps the worst disservice done to the Labour Party by the media has not been to exaggerate the roster of accusations against Corbynites, but rather to almost totally obscure the other half of the tally.

At the extreme end, there have been reports of violence and physical intimidation against leading Momentum activists. Corbyn himself has received multiple death threats. BAME Corbynites, most notably the Jewish socialist activist Rhea Wolfson, have also been the object of horrific racial invective online – and no, there’s no particular reason to think that the people behind this were anti-Corbyn Labour activists; but then, similar benefit of the doubt is never extended to Corbynites when their opponents are subjected to similar disgusting attacks.

Meanwhile, at ground level, rank-and-file members encounter abuse and hostility in the sprawling ecosystem of anti-Corbyn Twitter accounts and Facebook pages have been established in recent months, many of which play on every grotesque stereotype about Muslims, black people, immigrants, welfare “scroungers” and other social groups seen as part of the good-for-nothing, down-and-out pro-Corbyn demographic. One of them, a dating website parody called Momentum Matches – which has been retweeted by numerous Labour councillors and members – sets the tone with a picture of a Muslim woman, captioned: “Ayesha is looking for love with Momentum Matches. Likes: Allah, pies (all of them) Dislikes: Pigs, immodest attire”. Another photo, this time of a white woman, is labelled: “Giulietta is looking for love and a UK passport with Momentum Matches. Likes: working cash in hand, not being deported”. In other cases, whole accounts are explicitly based on racist themes, and yet they never seem to catch the attention of the Labour Right, let alone earn its condemnation.

At the centre of this lurid, bottom-feeding discourse-within-a-discourse is, of course, a fanatical and often violent hatred of Jeremy Corbyn himself. Not unrepresentative is one former parliamentary special adviser on Twitter – followed by Progress, Saving Labour and assorted Labour MPs including Tom Watson and Dan Jarvis – who calls her opponents “Corbynista scum”, the Shadow Chancellor a “Fucking piece of shit” and suggests that Jeremy Corbyn is a paedophile. And it is in this area – the matter of Corbyn’s personal character – that anti-Corbyn party leaders have been so strikingly irresponsible and negligent in their own rhetoric.

There has been a small spasm of outrage on the party’s Left (the Right has made no comment whatsoever) over a recent Mail on Sunday article, written by the Labour donor and former parliamentary candidate Michael Foster, which directly compares Jeremy Corbyn to Adolf Hitler. But the truth is that this despicable analogy has been completely mainstream among anti-Corbyn MPs, journalists and aides since before Corbyn’s leadership. The journalist Nick Cohen repeated it, in the liberal and respectable Guardian, only the other day. The Left is admonished for failing to “keep it comradely”, but anti-Corbyn Labour MPs were comparing the elected Left-of-centre leadership to a genocidal Nazi occupation as early as August of last year. Such talk is not only stunningly offensive, but dangerous and irresponsible.

In spite of all of the above – and of the radio silence on the issue from Owen Smith and his parliamentary backers – I have no interest in trying to pin responsibility on Smith for the disgusting comments made by some of his supporters. I won’t go poring through his political biography for the smallest footnote that I could somehow connect with the numerous people tweeting hate above an “Owen Smith” twibbon. What should concern every Labour Party member, whoever they plan to vote for, is the construction and mediation of a safe, respectful space for our debates and disagreements. That won’t happen as long as one side keeps pretending that abuse and bullying is a one-way street.