This is a challenging question to answer, given the information on voting at the state legislative level is so disparate, but I will do my best with the information I have.
Certainly we see that there is resistance at the state legislative level to provide public funding to religious schools from select elected officials, but it is challenging to compile the voting history of each representative ad-hoc to give you a full comprehensive answer.
With that in mind, we see, most recently, in South Carolina, a bill was recently introduced, H. 3591. This bill, proposed by the republican constituency, aims to REPEAL SECTION 4, ARTICLE XI OF THE CONSTITUTION OF SOUTH CAROLINA, 1895, RELATING TO THE PROHIBITION AGAINST THE STATE OR ITS POLITICAL SUBDIVISIONS PROVIDING DIRECT AID TO RELIGIOUS OR OTHER PRIVATE EDUCATIONAL INSTITUTIONS.
The South Carolina House passed the resolution (Yeas: 83; Nays: 27; Excused Absence: 3; Not Voting: 11), and data on the representatives opposed vs in favor can be found here.
One key opponent, Rep. Joseph Jefferson (D-Berkeley), voiced his concerns over the proposed bill, and also voted in line with his concerns.
I would love to build a more cohesive view of this, compiling first the current elected officials of a given state legislature, and then layering on their voting histories to collate a single source of truth for this type of data.
Full disclosure, I am currently building a site that compiles this data on the federal level(EG this is a SC rep's voting history at the federal level), but if enough interest is shown for this type of data at the state level I would be happy to pull it together.
Your question is very reasonable, and it's a shame that it is so difficult to give a more comprehensive answer to it.