I'm hard pressed to design a good, reproducible experiment on the question one way or the other.
> The field situation consisted of a park-bench discussion of a topical social issue, arranged by a public-opinion interviewer. Prepared experimental variations were introduced by one of the discussion partners, a confederate of the interviewer. In the critical variation, the confederate insulted the subject during discussion. In other variations, he tried to persuade but did not insult, or else simply gave certain arguments without intent to persuade. Attitude-change results supported the hypothesis of negative change in the insult condition.
Eleanor Gordon-Smith spent two years interviewing people who changed their minds, and suggests this:
> The strategy is this: Ask where people’s beliefs come from as well as what they actually believe.
https://www.marketwatch.com/story/this-is-the-difficult-secr...
The paper has been cited only about 40 times in the half-century since it was written, but I found one recent interesting citation:
https://www.researchgate.net/publication/327127198_The_Monta...
Uncivil remarks uniquely diminished the speaker’s reputation, and had little impact on the reputation of the targets of the attack, the perceived winner of the verbal exchange, the reputation of the speaker’s party, or the sense that the country is moving in the right direction. Incivility made the speaker seem less warm and did less to affect perceptions of dominance or honesty. This warmth deficit explained the reputational costs of incivility.
I'm skeptical of the study for a variety of reasons, mostly coming down to the issue of what people tell researchers vs what they actually do. But it's good to know that somebody is at least trying.
If I were trying to get moralizing conservatives to agree with me, then not insulting them would indeed be the first part of an effective strategy. However, I'm not trying to change minds, because that is also fruitless.
For the same reason that trying to convince ordinary people that their promiscuous lifestyles are bad won't actually change their behavior, trying to convince moralizing conservatives that their entire worldview is wrong isn't going to change their perspective.
This kind of person is not trying to achieve an effective outcome through policy, they're trying to use policy as a weapon against people they don't like. Debating the effectiveness of various policy options won't move that particular needle, so why bother?