Charles Coulombe publishes an article in the Catholic Herald asking this question, and noting its relevance for Catholics of Anglican patrimony. Here’s an excerpt:
Interesting as all these facts may be to students of English history and Anglican beliefs, what interest could the question of Charles I’s sanctity possibly have for Catholics? Quite a bit, really.
For one thing, his cultus plays a prominent role in that Anglican Patrimony which Pope Benedict XVI created the Personal Ordinariates to preserve within the Catholic Church. When various Eastern Orthodox groups have been reconciled to the Church, they have been allowed to continue to venerate a number of post-1054 figures as Saints. So, might our newly admitted brethren of Anglican background be able to do the same with Charles I?