Is there such a thing as a religious spirit? Is it a Biblical concept?
Obviously, the first part of this is that you cannot find it explicitly stated in scripture. Of course, there's also religious systems that contradict the deity of Christ (i.e. false religions) but where does this idea of a "religious spirit" come from when charismatics use it in regards to the Church?
I don't personally know how others define the term "religious spirit," but some have reduced the concept down to such things as a woman wearing a dress or a man wearing a suit and tie while attending church, or having structure to church services, or feeling the need to share from scripture during a church service.
In and of themselves, I would propose it's ludicrous to argue these are characteristics of a "religious spirit" at work. Here are some verses to look over in regards to this matter:
"Having a form of godliness but denying the power thereof: from such turn away." - 2nd Timothy 3:5
"Woe to you, scribes and Pharisees, hypocrites! You pay tithes of mint, dill, and cumin, but you have disregarded the weightier matters of the law: justice and mercy and faithfulness. Those you ought to have done without neglecting the others." - Matthew 23:23
"You blind guides, straining out a gnat and swallowing a camel!" - Matthew 23:24
"Woe to you, scribes and Pharisees, hypocrites! For you clean the outside of the cup and the plate, but inside they are full of greed and self indulgence." - Matthew 23:25
Much of what these verses refer to is flat-out hypocrisy.
Both Jesus and Paul are describing people who look good in a religious sense, but whose hearts are corrupt and they're putting their confidence in a religious expression.
All the while, they're still bound on the inside without power.
Look at the intensity of this rebuke from Jesus to those who put greater emphasis on religious formula than the inner transformation of a heart connected to God:
"Woe to you, scribes and Pharisees, hypocrites! For you travel across sea and land to make a single proselyte, and when he becomes a proselyte, you make him twice as much a child of hell as yourselves." - Matthew 23:15
It's not as if Jesus was opposed to following the scriptures, though. He even stated that He didn't come to abolish the law but to fulfill it! His harsh condemnation was not against external religious expression - He reserved His rebuke for external religious expression that was not accompanied by the inward reality of the life of God within the heart of the believer.
"You search the scriptures because you think that in them you have eternal life and it's they that bear witness about me. Yet, you refuse to come to me so that you may have life." - John 5:39-40
Jesus is not opposed to people studying the scripture - His life was rooted in them! We see him in the temple at the age of twelve, sharing the truth of scripture with the religious leaders of that time. He would even quote scripture from what we would now call the Old Testament.
Furthermore, when Jesus was tempted in the desert by the Devil, He resisted with scripture! So, He's obviously not opposed to the reading and studying of the scripture.
What He apparently was opposed to was using scripture as a mere religious external adornment to replace the reality of a living relationship with God Himself. Jesus appears to be saying: "Please, read the scripture, but understand that scripture points to me. Don't read it as a religious end, in and of itself! Recognize that it points to me and come to me, so that you may have life."
Mere religious systems that have form without power are very big on words. While not denying the truth that our words are important and that words are also important in theology, we must recognize that what God has for us is more than mere words.
Look at what Paul says in 1st Corinthians 4:20, "For the Kingdom of God does not consist in talk but in power." What a statement!