A conservative couple won't use a sperm donor. The woman will literally be carrying another man's child, not her husband's.

What makes you say so? They wouldn't adopt a kid too? I don't think it's a "left" issue at all for couples. For single mothers, maybe

Adoption is different if done properly. The adopted child should not in anyway be implied or declared to be of the same bloodline as the adopting parents, otherwise we'll end up with the same issue seen here. It's also important that the child know that they're adopted from early on, and not hide that fact.

Whereas artificial insemination is literally having the woman carry another man's child, it goes against conservative values (would they let another man sleep with the woman to impregnate her if there weren't artificial insemination?)