Years ago, soon after I had become vegetarian (today, 'soon' implies within my first ten years of being vegan), an animal advocate* phoned me with the 'urgency' of feeding stray cats who had found their way into the basement of the local Adventist church building. The church building was only used intermittently during the week (but it was used and sometimes the basement was rented out to other church and vegetarian groups), so the congregation didn't want to pay staff to care for these stray animals (who were there, not because the congregation had borught them in, but, according to Beth, because "God had brought them there to challenge the congregation to become more loving to animals").
*the late and once very strident-voiced Beth, who considered herself a Christian vegetarian, but whose 'Christian vegetarianism' was limited to blaming organize religion to not doing right by animals (perhaps you've seen that happen as you meet people)
Well, we drove over to the otherwise vacant church building and nosed around, trying to see at least one now-sheltered animal pawing through the basement; we could not. But Beth uttered one vitriolic comment after the other about the cold, heartless, cruel, congregation who wouldn't care for these cats and had decided, after a week of deliberations and the inability to get them 'adopted out', to have them euthanized (I guess that local shelters were full).
Beth's heart was exercised; she was distraught, and I could worry about Beth's health because she was elderly (looked about 20+ years younger on a vegetarian diet, but she let herself get SO dreadfully worked up on such issues that I feared she'd lose that entire 20+ years of 'slack' on the stray cats).
I guess that the cats were euthanized, and later, Beth died (presumaby, NOT because of her emotional work-up over the cats because she lived several decades after this, equally worked up over other 'issues' of animal suffering.
My point is that suffering is one fo the several issues on a multidimensional axis; overt cruelty is another dimension; other issues are on that multidimensional grid, whether or not we realize them.
"Whatever we decide needs to improve sustainability of the overall situation."
Beth did not offer a sustainable solution that worked for everyone (including farmed animals); few 'pet companions' offer any real, long-term solutions, either.
Pet 'ownership' or 'companionship' (as if changing the noun we use for these situations makes a material difference) may not be sustainable; animals in the wild are in a real pickle, also, as are humans in the developing world.
Choosing within ourselves to NOT cause harm overtly is one choice we can make; we can make a difference today by becoming vegan, BUT that choice will not resolve ALL suffering lf ALL other persons, but neither will giving money to 'animal protection' organizations (and it might actually pay them to do things which perpetuate the wicked system of food production and animal exploitation and abuse, and like neuroses in otherwise mentally healthy persons, their rationales may merely cover up the wrongs they are doing so that not even they are able to admit or acknowledge these wrongs and injustices to themselves, or within their own minds.
What should a Christian church do? a VEGETARIAN Christian church in which at that time a large number of the congregants may have been vegans?
That's a discussion topic.