Are strobe lights allowed in red signals?

No. Section 4D.06 of the 2009 MUTCD specifically prohibits strobes within or adjacent to any signal indication.
There is no deadline for existing strobes to be removed, but no new installations are allowed to be made.
Resources
Manual of Uniform Traffic Control Devices (MUTCD). Frequently Asked Questions – Part 4 – Highway Traffic Signals. FHWA