P-values for group comparisons in tables for patient characteristics/demography should not be used either in RCT´s nor non-RCT´s. If one still would like to do some kind of comparison between groups, what are your thoughts on using effect size (Cohens D, Cohens H and Cramers V, etc) ?
You are emphasizing linear statistics. I would go with empirical cumulative distribution functions stratified by group, if you need univariate comparisons. Univariate comparisons are often misleading.