Not necessarily.
I know you were referring to Catholics here, but “charismatic” and “traditional” go together a lot more than they disagree, across the denominations.
The traditional Catholic is, or maybe used to be, off put by some of the unfamiliar forms of charismatic worship. However, when the traditional Catholic, or traditional Lutheran or Anglican, show up to picket the abortion clinic, they may well find themselves next to charismatics. Traditional Christians of all types tend to emphasize the supernatural, the transcendent dimension of doctrine, worship, healing, and practice of Christian life.
So do charismatics!
When Pope Francis speaks about the reality of Satan acting in the world, I bet that rings a bell of familiarity and agreement both to traditionalists of all stripes, and charismatics across the board of Christianity. This puts both groups on one side; on the other side are liberal Catholics and Protestants, who believe all the problems of the world can be solved by equality, discussions, standardized testing, and more government.