I see this come up a lot on this board and want to offer up a couple of examples from my experience that bolster the case for working with a range of voices on a single issue. (I'd welcome counter examples, as I genuinely want to unpick this for my own sanity!)
Example #1: Named Person law
In Scotland, the SNP Govt passed a law (supported by all the opposition parties bar the Tories) that would have assigned every child in Scotland a state guardian. Please Google for more details if you're interested.
A groundswell of grassroots opposition rose up to challenge this law and it was largely fronted and resourced by a Christian group (forget the name of the organisation). They set up a campaign group (No2NP) and were joined by a children's law centre and a former senior social worker but the Christian group were the driving force.
I could see this law was an affront to civil liberties and yet Liberty were nowhere to be seen (waves at Shami). My most generous interpretation is that Liberty has no real presence in Scotland so weren't up on it all. Nonetheless, no human/civil rights groups spoke up.
Anyway, lots of my left-leaning, liberal mates tried to warn me off supporting the campaign, because of the Christian group and what other causes they had supported.
But the campaign group ploughed on, took a legal case and were vindicated in their concerns by the UK Supreme Court.
Example #2: EU referendum
I spent some time campaigning for Remain and most memorably spent a few hours in my hometown leafleting a few days before the vote. Standing on the same block were a former senior advisor to the Tory party, an SNP member and a lifelong Labour voter.
That individuals with very differing (often oppositional) politics could come together to fight for the same issue I found really moving. I remember too a photocall of Cameron, Ashdown and Kinnock doing a stint on a Remain phonebank, and felt similarly moved.
Meanwhile, Jeremy Corbyn refused to share a platform with any Tory or even (horrors) Brown or Blair. Of course, we can only speculate here but you have to wonder if we would be where we are now had he not taken such a puritanical view re engaging with the main Remain campaign.
If we indulge the culture wars narrative, aren't we ourselves just being complicit in the polarisation of politics, which is what's got us where we are today (Trump, Brexit etc.)?