Sadly I'm not so sure that the the 'red/green divide' is always an argument amongst people who all want the same thing
Take the UK for example
In the UK many of the most vociferous anti-hunters are motivated by political and class hate, not conservation.
If it wasn't hunting they'd find some other justification to hate those they've been taught to believe are "the enemy".
Environmentalism is the current in-vogue band-wagon for people whose purpose in life is to nurse an invented grievance. For them environmentalism/animals rights are the vehicle, not the cause.
Sadly, in the UK, the only voice we hear is that of these militants
Not all those who find hunting distasteful are politically motivated however - it is to these people we need to direct our efforts We need to explain that the greatest threat to wild places, wild life, natural habitat and biodiversity, wherever it is to be found, whether in wilderness or managed countryside, is human encroachment, human disturbance and human industry.
We need also to explain the role of the hunter in providing funding for the maintenance of wild protected areas and their role in giving wildlife an economic value, without which (in this human centric world) it will not survive.
Perhaps some will listen