While this would create a hybrid genome it would be a simple compilation of two haploid genomes that are still separate so there would be a large amount of duplication of sequences, which will cause issues with almost all reads multi-mapping. If @ssjima2014 is looking at a hybrid of those two parental strains then the hybrid genome will be recombinant of the two parents, so alternating parts will be identical to parental genomes.
Note: It is not clear to me if a genome assembly is available for C57BL_6NJ_v1 hybrid directly at EBI.
What exactly are you trying to do here? Is this a hybrid of two known parents (C57BL and 6NJ) ?
Have you checked a few reads that do not map to make sure they are still mouse and not some contamination.
For RNA-seq, 65% aligned reads is actually within the normal range. That fraction can change substantially depending on the sample prep, such as RNA quality and library kit.
Different strains should not be that different.