I think the particular issue with the dog meat industry is that it has high amounts of cruelty, even by meat industry standards. Iirc there’s the belief involved that if the dog suffers it makes the meat taste better. So at many farms they are often tortured before death and killed in painful ways. They are also kept in horrendous conditions. Farm animals are often kept in horrendous conditions as well, but generally that’s because of a lack of regulation and most people who oppose dog meat farms also oppose the mistreatment of farm animals as well.
Well the earliest I can think of christians getting in to politics is ancient Rome, but I’m sure it’s been happening since before then too. As for the US, something tells me they’ve been involved from the start, regardless of what the constitution says.