Do housekeeping genes vary between tissues
My experience is: Yes they can vary quite a lot (according to differences in the genetic profile of the cells) and you have to test this. As a primer I can recommend reading the articles listed below. These are mostly looking into this in the context of realtime PCR, but this should be valid for RNAseq as well. For some applications it is also a good idea to use more than one gene for normalization.

References:


Accurate normalization of real-time quantitative RT-PCR data by
geometric averaging of multiple internal control genes.
Selection of housekeeping genes for gene expression studies in human
reticulocytes using real-time PCR
Reference Genes / Housekeeping Genes
Gene Ontology Based Housekeeping Gene Selection for RNA-seq
Normalization