Well first, the OP asked if there were ANY religous groups that encouraged scientific inquiry. A few examples (heck, even a single one!) are sufficient to show that there are.
I think that distinction is both false and irrelevant.
Irrelevant, because science pertains to the physical universe and religion pertains primarily to spiritual matters. While there can be some overlap (for example, when miraculous claims are made), their realms are mostly separate. For example, how would one scientifically determine that it is wrong to rape little children, or to steal from one’s neighbor? It can’t be done, since such questions do not lend themselves to scientific inquiry.
Additionally, despite the protestations of many on this board, religious faith does not (necessarily) mean abandoning all observation and evidence whatsoever. That’s certainly not what the New Testament writers meant by faith. Matthew, for example, repeatedly appealed to the alleged fulfillments of Old Testment prophecies. One might disagree with Matthew’s intepretations of these prophecies, or their alleged fulfillments, but the point remains – at no point did he ever say, “Look, just trust me! Don’t ask for any evidence, just trust me!” Nor did the Apostle Paul, for in Acts 17:17, he is said to have “reasoned in the synagogue with the Jews and with the Gentile worshippers, and in the marketplace with those that happened to be there."
Jesus himself is recorded as having healed a paralytic “so that you may know that the Son of Man has authority on earth to forgive sins…” (Matthew 9:6). Again, a skeptic may disbelieve this account, but the point remains… According to the gospels themselves, Jesus did not expect people to believe by abandoning all evidence.
Then you have people like Sir William Ramsay, Dr. Simon Greenleaf, C.S. Lewis, Lee Strobel, Peter Stoner, Frank Morison and more… People who came to belief through investigation of the scientific and historical facts. These people are highly respected within Christianity. Several of these individuals even sought to disprove the case for Christianity, and yet were forced to conclude that Christianity was worthy of belief. Again, one might disagree with their conclusion, but that’s ultimately irrelevant. The point is that Christian faith does not require that one ignore all evidence and take a blind leap of a cliff.
Even Jesus is recorded as having performed