For example, in my current project assessing the impact of health care intervention on # hospital inpatient visits compared with a control group, age and sex are moderators that could influence the relationship between the intervention and the outcome.
Is standard practice to match on moderator variables just as you would a confounder?
Or match on interaction effects for moderators and confounders (e.g., age_category $\times$ healthy_living_motivation_score and sex $\times$ healthy_living_motivation_score)?
I would think by default if you match on a moderator and a confounder, you are also matching on the interaction effect of the two variables.