It is important to know what the Left is, and that it has evolved.
(See references below)
The Left is now mainstream, and almost universal, in the West - e.g. in 2010 Britain had a Leftist 'Labour Party' government replaced by a Leftist 'Conservative Party' - and there is absolutely no difference between them in terms of Leftism - indeed, in legally-'redefining' marriage - it was the Conservative government which forced into legislation the biggest piece of extreme Leftist legislation in recent decades.
So, at present in the West; the Left is essentially everyone with power in public life - the only non-Leftist groups are relatively-small traditional religious denominations.
The Left is, in its origin, the reaction against Western Christianity. Which means that Leftism is not a specific set of doctrines or beliefs, but a reaction against a religion - and therefore the Left has changed, and evolved - and become a very different thing at different times and places in history.
But many people are confused by the fact that the Left has changed. For example, it is said that the US or the UK are 'communist' countries... This is true in one sense, but completely false in another - because modern Leftism in the West is up-front very different from Soviet, or Chinese Communism.
The fact is that throughout the success of Leftism in the West, Leftism has evolved; and this is no accident, but is in fact the primary reason for its success. The Left responds to the situation, and as it succeeds in defeating Christianity it changes its strategy in order to eradicate the latest problem.
Leftism was initially very clearly anti-Christian (often anti- the established church). The biggest change in the Left happened in the mid 1960s. (But of course there is a grey area, and change was gradual - even though it was swift.) Up to the sixties, Leftism was about 'rational' economics - nationalization, planning, meritocratic equality of opportunity etc; but after the sixties the Left was about culture - and in particular the sexual revolution - equality of outcome, and the fluid agenda of antiracism, feminism, and more recently the multi-culti/ diversity/ inclusive agenda.
This was a massive change in doctrine - and a change from a revolution to establish an eternal utopia; to establishing a state of permanent revolution with no end-point.
My point is that the Left has evolved and transformed - but there is continuity, and that continuity is that the Left is an opposition, a reaction - the Left is 'against' not for. And the main thing the Left is against is Christianity (real traditionalist Christianity, of any type); and against everything to do with Christianity.
Why else is the redefinition of marriage regarded by both sides as such a major victory for the Left? It is a major victory because it represents a massive blow against Christian morality - more exactly it all but completes the elimination of Christian morality from the legal systems of the West.
(Of course, another strategy of the Left has been to subvert the Christian churches, to make them non-Christian, indeed anti-Christian. Most mainstream self-identified Christian churches have been reconstructed - as evidenced by their support for the sexual revolution and redefinition of marriage. Indeed one of the greatest triumphs of the Left has been thereby to discredit Christianity as being the original source of the Left! So that in some secular circles - among those who imagine themselves to be opposed to Leftism - Christianity is damned when it succeeds and damned when it fails! Damned for being a cause of Leftism, damned for weakly capitulating to Leftism!)
But if the Left are currently obsessed by redefining marriage then who else in The West would care about traditional marriage (i.e. real marriage) except Christians? The Old Left, pre 1965 - would have considered a focus on sexuality and identity politics trivial and immature - they were focused on rationally restructuring society, encouraging and exploiting technological breakthroughs, efficiency and effectiveness...
The modern emphasis on this issue and other sexual issues is revealing of the covert and often unconscious agenda of the 'New' Left, which reveals what it shares with Old Left - that the Left is not for anything in particular, but it was, and still is, orientated against Christianity, especially Christian morality - and that is why and how the Left has evolved.
The Left becomes whatever is effective against Christianity, even when that Christianity is residual. Over the decades, the Left has evolved to defeat one defense of Christianity after another. And it has been able to do this precisely because the Left is indifferent to what kind of society it creates, and is indifferent to what level of chaos and destruction it engenders - it simply changes its attack until it finds something effective against Christianity, and if the attack fails the Left will change again.
There Left has no consistency or coherence, and no need for consistency or coherence - consistency and coherence just get in the way of attacking Christianity by any and every means.
The Left evolves, and Christianity is what the Left evolves around.