This is the wording from the RAH contract:
The Company will not transfer any Company aircraft or schedule
any pilots to fly any trips for airlines that are on strike unless
mutually agreed by the Company and the Union.
The way I read it, in the absence of specific guidance to the contrary from the striking mainline union (such as was mentioned above regarding NWA's '98 strike), if it is in that company's paint, it doesn't move.
The RLA also permits secondary strikes.