If you've been accused of having a "religious spirit" it probably means you're like the Bereans (Acts 17:11) - that's a compliment. This accusation is commonly used to justify an unbiblical teaching, new revelation, demonic or manufactured manifestation (gold dust, glory cloud, angel feathers, etc), or some mystical encounter with God or an angel. You will be accused of “having the appearance of godliness, but denying its power” (2 Tim 3:5). Conveniently, they will ignore the rest of the passage: “while evil people and impostors will go on from bad to worse, deceiving and being deceived. But as for you, continue in what you have learned and have firmly believed, knowing from whom you learned it and how from childhood you have been acquainted with the sacred writings, which are able to make you wise for salvation through faith in Christ Jesus. All Scripture is breathed out by God and profitable for teaching, for reproof, for correction, and for training in righteousness, that the man of God may be complete, equipped for every good work.” (2 Tim 3:13-17).
Most of these accusers have been deceived by imposters - modern day "apostles" and "prophets" who masquerade as servants of God but are actually servants of Satan (2 Cor 11:13-14).
It's the accusers who have a "spirit" that's false:
"For if someone comes and proclaims another Jesus than the one we proclaimed, or if you receive a different spirit from the one you received, or if you accept a different gospel from the one you accepted, you put up with it readily enough." (2 Corinthians 11:4).
