It's all true.

The (pre-modern) Japanese word for card games is Karuta, which comes from the Portuguese word for cards (carta).

And yes they were banned. In 1597 Chosokabe Motochika, the daimyō of Tosa, banned them, which seems to be the first incident of cards ban in Japan. The Edo Bakufu also banned them. The bans were because of gambling, not because they were foreign. The laws states gambling as the reason. The Edo Bakufu banned other gambling games too. Sugoroku (a game similar to backgammon) which has had bans issued repeatedly every since Empress Jitō issued the first recorded ban in 689, obviously to no avail. Even Mikasazuke, a poetry competition game, was banned for its popularity in gambling (sorry, I don't know how the game works).

The repeated bans didn't work (surprise, surprise) and gambling continued in supposed secret, along with the development of various different gambling decks. Non-gambling decks though, were developed, with the game idea of matching pictures or poetry, which are still played.