Richard Allen's murder trial is set to begin on May 13.
He is charged in the 2017 murders of teen girls Libby German and Abby Williams.
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Prosecutors are asking the judge to ban words like "Odinism," "cult" and "ritual killing."
They say if the defense uses those terms, it could confuse the jury.
This comes after the defense team claimed people with ties to "Odinism" had a motive to kill the girls.