I am a Catholic and I do think this crosses the line established for non profits regarding political activity.
If the Cardinal wanted to have cards about immigration passed out it should have been one that simply stated the USCCB's statement on immigration with a plea for people to remember Catholic teaching when contacting politicians about the immigration debate.
There are few issues that Catholics must adhere to / believe to remain loyal to the Church, and immigration isn't one of them. Ironically, pro-life being one of them. So for him to refuse the pro-life petitioning is shameful.