Thank you for your question. There are no particular strictures set forth in the way that you suggest (as to denomination, e.g.), although the session is specifically charged in this way in the Directory for the Public Worship of God:
The session is to give diligence that no person enter the pulpit concerning whose soundness in doctrine and life, or knowledge of Scripture, there is reasonable doubt. (DPW 2.A.3.c.)
Elsewhere, the session is given general oversight of the worship:
The session is charged with maintaining the government of the congregation. It shall oversee all matters concerning the conduct of public worship … (FG 13.7)
… further cementing its role in “guarding” the sacred desk (to use historic language).
All this is to say that while our Book of Church Order does not presume to dictate to sessions who may enter the pulpit (as to his denomination or the like), it does charge and give oversight to sessions in the ways noted above. Particularly, the stricture in the DPW (cited above) means that only men known to be sound (in life and doctrine) should come into the pulpit and, by extension, only sound preaching (in keeping with the Scriptures and our doctrinal standards) should be heard in our pulpits.
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