Many Christian theologians attempted to demonstrate the existence of God rationally, so I don't know what about that process would have been considered heretical in its own right. I'd agree that the claim (associated with Deists, for example) that one could have a complete religion based exclusively on reason with no revelation, or that all purported divine revelations are untrustworthy, would have been considered heretical.
The first rabbi who goes the above path - and during his time, his books were often burnt.
It still is, according to Catholicism, which says you must have reason and faith in the divine revelation it claims to preserve, which reveals some aspects of God and reality that we cannot reach or conclude with pure reason alone, such as the Blessed Virgin Mary's Immaculate Conception (BVMIC for short) or the Trinity (T for short).