I think it would be “un-Catholic” yes, since why would you want to limit universal suffrage, This would imply that you (and I don’t mean you personally I’m using it in a general sense) desire to take away this right from certain groups of people, either because of their gender, social class, religious profession or else. This would unfairly infringe upon the human dignity of certain groups of people, giving them absolutely no say in the running of their country.
In Christ there is neither male nor female (gender discrimination), Jew or Greek (racial and religious discrimination) or slave or free (social discrimination). Christ has broken down these barriers. This doesn’t imply that everybody is the same, but it does imply a basic equality amongst all people and the right for all persons to be treated fairly and in accordance with their dignity as human beings made in the image of God.
To prevent universal suffrage then, would in my opinion highlight an underlying prejudice on the part of the governing authorities towards certain groups of people among the public.
Certainly this is not defensible according to Catholic teaching, St Thomas aquinas stated quite plainly as above that: “All of the people should take some share in the government”.
It should also be noted that Pope Leo XIII, in an encyclical on Catholicism in America, praised the “popular suffrage” (as he called it) which underlined the American Revolution and brought about the United States:
“…We traverse in spirit and thought the wide expanse of ocean …] To this We apply Ourselves with the utmost zeal and care; because We highly esteem and love exceedingly the young and vigorous American nation, in which We plainly discern latent forces for the advancement alike of civilization and of Christianity …] For when America was, as yet, but a new-born babe, uttering in its cradle its first feeble cries, the Church took it to her bosom and motherly embrace …] Nor, perchance did the fact which We now recall take place without some design of divine Providence. Precisely at the epoch when the American colonies, having, with Catholic aid, achieved liberty and independence, coalesced into a constitutional Republic the ecclesiastical hierarchy was happily established amongst you; and at the very time when the popular suffrage placed the great Washington at the helm of the Republic, the first bishop was set by apostolic authority over the American Church…”
- POPE LEO XIII LONGINQUA (ENCYCLICAL ON CATHOLICISM IN THE UNITED STATES), 1895
Now, in terms of voting, the US did not obviously have universal suffrage at this early stage, however it was an early antecedent to the idea since it was a popular revolution against Great Britain, that was supported by most of the population, who also popularly wanted Washington to lead the nascent country.
In fact, somewhat embarrassingly for a modern democracy, the US did not get complete universal suffrage until 1965 since many Southern states discriminated against African Americans. The UK got universal suffrage in 1928