The answer is given by the properly-formed question: Is Christianity inherently left-wing compared with what?
(And I mean compared with actual, real, historical situations - not with wish-list collages of 'these are the things I would like best in my perfect society' compiled by intellectuals.)
Have radical Left leaders over the past centuries been famous for their orthodox Christian devoutness; or for their atheism, heresy, liberalism?
Are the most Leftist regimes of all all time (i.e. Communist) characterized by their promotion of orthodox Christian devoutness; or for their subversion, persecution, imprisonment and mass murder of Christians?
And so on.
Mainstream modern Christianity is, of course, mostly led by Leftists - but then what isn't? The ruling elites just are Leftist. If you are not Leftist, then you are not a leader of anything powerful.
But the debate is arbitrarily framed.
Someone comes up with their own personal, imaginary, ideal list of what it would be to be reactionary - then measures up real world things against that list.
But if reaction has reality, if the polarity between Left and not-Left has reality, then this procedure is nonsense.
We would, instead, need to perceive the diversity of actuality as imprecise and imperfect representations of underlying trends.
And these trends - of which actual political realities are imperfect representations, are:
A 'traditional' society organized around religious imperatives (of which Christianity is one) - this is The Right.
A 'modern' secular society organized around the pleasure-pain axis, a utilitarian society, a this-worldly society. This is The Left.
Real life is, of course, much more mixed-up and compromised and corrupted - but these are the underlying realities.
Those who reject religion (of all kinds) are Leftists (differing only in strategy and priorities); and those who advocate a society which is ruled by religious imperatives are The Right (differing - profoundly - in their understanding of the Truth by which society ought to be organized).
And the rest are just sophomoric pick-and-mix wish-lists - intellectual collages.