Everything that people own has some carbon cost associated with is, so the mere presence of a carbon cost doesn't justify getting rid of it.

Why would you argue that pets specifically are something that people should give up? People have needs that go beyond food, water, and shelter (e.g. play, love, stimulation, etc.) that will have to be factored into any plan to reduce carbon emissions. It seems to me that pets are an excellent value in terms of degree to which they provide for their needs versus associated carbon cost.

Yes we have needs, but the planet has limits that we already hit, so we now should all have a moral duty to limit/filter our non-essential needs

The sources show how significant pets impact is (1/5th of the world meat+fish production, think about the processing, transport, and all intermediate materials required for this and the pollution that generates, and finally the ecosystem damages via outdoors and feral ones)

I see what you're saying, but I'm not sure that the needs that pets supply are non-essential. For many people they are a significant, if not primary, source of companionship and joy. I think we would need a plan for how to offset removing something so important.