It will depend on the gene. It would be great if there was an easy tool to use like Primer-Blast that let you pick the mouse substrain to design qPCR primers and look for potential "off-target" cross-reactivity.
This recent paper describes some recent database refinements for the commonly used strains:
https://www.nature.com/articles/s41588-018-0223-8
I imagine that in 99% of cases, you will find that if you test the top 2-3 of Primer-Blast suggestions you'll find a good primer pair, so it might not be the best time investment to build such a tool, but of course being careful is important to avoid embarrassing mistakes that could have been avoided.