This is a question that comes up quite frequently and appears to be a source of some confusion. The law is that motions to strike a state law claim are proper in California Federal courts, e.g., libel, slander, intentional interference with prospective economic advantage. This is so because there is no conflict between the Federal rules and Code of Civil Procedure 425.16(b). Plus, it furthers the purposes of the Erie doctrine.
However, there are some important limitations of note. First, a court may not strike a federal question under the anti-SLAPP statute.
Second, the discovery limiting aspects of 425.16(f) and (g) may not apply.
There is a bit of a split of authority on this issue. Some courts have held that (f) and (g) directly collide with Rule 56 and others have not. For example, the Central District held that there was no collision between Rule 56 and (f) and (g), whereas the Eastern District believed there was. In fact, the Eastern District announced a test to determine whether a court could apply (f) and (g) where either of the three scenarios applied: (1) the factual basis of the case has been developed through discovery or similar prior proceedings to the extent a motion for summary judgment would be appropriate; or (2) the parties agree that further discovery is not necessary, or (3) the only issue presented by the motion is an issue of law and the motion is suitable for decision as a motion to dismiss pursuant to Rule 12(b)(6).
This information is important alike to SLAPPers (defendants) and SLAPPfeasors (plaintiff) for obvious strategic reasons.
Choose your forum carefully, if you have the option to do so.