I believe that appeal to religion here is futile. The moral foundations of liberals and conservatives are very different and it is easy for conservatives to dismiss the liberal moral foundations as it is easy for liberals to do the same about conservative morality.
Let's reverse things and have a conservative group of religious people try to appeal religiously to liberal believers and we will see that it won't work either. For example, would a campaign from religious conservatives to change the religiously liberal's hearts on "virtues of chastity" or what they call "control of desires" work? What about "social order" and "proper role fulfillment" that are so important to conservative morality? Would appeals to that work to reach out to liberals? The answer is no.
In other words, I can see how the liberal religion leaders appeal to fairness, compassion, social justice, equality, etc. to change a conservative politician's mind will NOT work.
Religion empowers people to derive their morals from it, be it respect for authority, gender role, social order, etc. on one side or social justice, fairness, compassion, etc. on the other side. However, one important thing to note is that, without religion and scripture, you can easily defeat and eradicate the backward stuff that a Paul Ryan and other like-minded religious people can use to derive their values from.
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