Is it possible that the Archbishop of Canterbury is secretly plotting to overthrow capitalism?

Perhaps he is covertly in league with a far-left revolutionary group and has been hiding a copy of Mao's Little Red Book inside his Common Worship lectionary. Maybe his core creed is less about loving and more about Lenin.

I only ask because according to one US-based columnist, Justin Welby is a 'Cultural Marxist'. Washington journalist Dennis Lennox, writing on The Spectator UK website a few days ago, claims: "Earlier this year, Welby took the Cultural Marxist line when he appeared to equate the church's historic propagation of the gospel with the evils of colonialism."

Is this a fair claim? And what, in any case, is 'Cultural Marxism'? The answer to that second question is that originally it was an early 20th century idea popularised by something called the 'Frankfurt School' – a body of German intellectuals, academics, and political dissidents which convened between the two world wars.

Sarah Manavis has summed up its main tenets succinctly as follows: 'The idea was that Marxism should extend beyond class and into cultural equality... The only way to destroy capitalism was to destroy it in all walks of life; where, not just classes, but all genders, races, and religions could live in society equally.'

So is this something Justin Welby espouses? Most would probably agree there is little evidence Justin Welby is aiming to 'destroy capitalism in all walks of life' – although it could certainly make for an exciting General Synod if he stood up and announced he was! At the same time, the idea that 'all genders, races, and religions could live in society equally' might well be seen as having some affinity with Christian belief that every human being is made in the image of God and therefore worthy of dignity and respect.

But hang on a second... There's also something a whole lot more sinister going on here. For the term 'Cultural Marxism' was popularised in recent years thanks to the Norwegian mass murderer Anders Breivik. Before killing 77 people in 2011, he wrote a 1,000-page document which refers to 'Cultural Marxism' 650 times.

One wonders if Lennox was aware of this horrific link when he wrote his Spectator article.

It appears to have been partly at least through Breivik that the term moved beyond the world of philosophy and into the popular online sphere. Nowadays it's often used in alt-right circles as a label to dismiss anyone with even a hint of the left-wing about them, according to Samuel Moyn, a professor of Law and History at Yale.

And let's investigate the specifics of Lennox's claim, namely that Justin Welby "appeared to equate the church's historic propagation of the gospel with the evils of colonialism". Did he? I don't believe so.

Read through his entire talk and what he simply seems to be doing, in a nutshell, is pointing out the need to be sensitive when engaging with people of other faiths given how they may perceive Christians for historical reasons. His argument is far more subtle than a simple equation of evangelism and colonialism.

So two things transpire: Firstly, the term 'Cultural Marxism' often has rather unpleasant connotations in the online world, whatever its origins, and is only to be used with great care. Samuel Moyn has described the term as a "crude slander". Secondly, the substance of the accusation against Justin Welby's talk seems incorrect. He wasn't advocating 'Cultural Marxism' but cultural sensitivity, which is a wholly different sort of thing.

Last year, the respected US Christian minister Tim Keller was also accused by some of being a 'Cultural Marxist'. In response, theologian Carl Trueman wrote: "While respecting him as a brother in Christ... I disagree at points with both his theology and philosophy of ministry... But he is no cultural Marxist, and to call him such is to reveal... the ignorance of the troll. It is to indulge in the spirit of this age, which eschews thoughtful argument about difficult issues for moronic and often malicious soundbites.' Trueman added: 'It is... a cheap way of pre-emptively delegitimizing him and his opinions... And – I almost forgot – it is to break the Ninth Commandment about a Christian brother."

Welby's lecture is worth reading. Not all of us who read it will agree with everything in it. But there is plenty of food for thought. At one point he says: "The issue is not evangelism per se. We try to persuade or commend things to others all the time, and in lots of different ways. The issue is whether we treat the other person seriously or not."

I like that. How might all our online contributions about others be different – whether writing columns or just offering comments on websites – if we took to heart the injunction to 'treat the other person seriously' first?

David Baker is a former daily newspaper journalist now working as an Anglican minister in Sussex, England. Find him on Twitter @Baker_David_A