The biggest critique of Kasich's faith is when he uses it from a economically-liberal vantage point. Evangelical conservative David French took issue with this line of Kasich's-
I had a conversation with one of the members of the legislature the other day. I said, ‘I respect the fact that you believe in small government. I do, too. I also know that you’re a person of faith.
Now, when you die and get to the meeting with St. Peter, he’s probably not going to ask you much about what you did about keeping government small. But he is going to ask you what you did for the poor. You better have a good answer.
The big bone of contention for French was for Kasich getting Ohio to go along with accepting federal funding to expand Medicaid as part of "Obamacare" and to do so quoting scripture from a liberal perspective
The ACA is a Rube Goldberg mess that started with a noble goal of getting health care coverage to the working-poor, but did multiple contortions to try to appear to be "revenue-neutral", messing up the private insurance system in the process.
However, we're stuck with it as long as that old man (a day older than I) has his keister in the Oval Office. What Kasich was largely faced with is the question "Should we accept federal help getting health care to the working poor?" Obamacare was going down with or without Ohio's consent on Medicaid expansion, leaving the Medicaid expansion part as the primary marginal decision for a state government.
The parallel question, shorn of the pork-barrel effect of free-money from Washington is "should the Federal government be paying for health care for the working poor in the first place?" Modern conservatives tend to want the Federal government to deliver the mail, protect our shores and stay the hell out of everything else (to borrow from WI governor Lee Dreyfus), so the reflex response on the right to the question is "Hell, no!"
However, I don't recall any Biblical commands to maximize GDP.
My core theology of economics (if I can grab a 2003 post) has two aspects; (1) we're supposed to help the poor and (2) we're selfish sinful critters save the Holy Spirit's intervention. Free markets are a good way to harness greed in a productive way in that sinful world, but a certain amount of government is beneficial in both pursuing the general public good and helping the needy. That begs for "limited government" but exactly how limited is an open question.
Should that include covering most of the health-care tab for folks making under $25K/year or so? You can make a case for that, especially if shorn from an Obamacare context. A Catholic-style preferential option towards the poor would be poised to answer in the affirmative. That's one that has a number of scriptures to back it up, although the scriptures on caring for the poor adress voluntary charity rather than the forced-charity of taxes.
However, we also need to take into account that the taxes and regulations needed to get it done damage to the economy and that the good generated needs to weighed against the damage done in the process of doing the good works. That type of marginal utility analysis is more art than science and has a lot of room for debate.
Modern conservative thought has a preferential option for low taxes and a free market. That makes Kasich's invoking that other preferential option (although not by name) sound somewhat sanctimonious to a modern conservative. It may well be sanctimonious and a bit of a Liberal Theocrat to borrow from French's title, but religious conservatives are used to having those terms tossed at them unfairly on a regular (probably daily for a public conservative) basis.
If you're doing your best to follow God's will and follow His word, you're going to get flak, sometimes friendly fire from fellow believers. I'm not sure if I would have made the same decision as Kasich, but I can see the logic behind it and respect it.