but I'm wondering whether all the Slavic people used the Cyrillic script at some point in their history?
Even if we include the Early Cyrillic alphabet, which according to Wikipedia was commissioned in the 9th century AD, then the Slavic language family predates the alphabet by around two thousand years.
The secession of the Balto-Slavic dialect ancestral to Proto-Slavic is estimated on archaeological and glottochronological criteria to have occurred sometime in the period 1500–1000 BCE
This means that many languages/dialects/etc would have been spoken without ever having been written down in the Cyrillic alphabet.
Take for example Czech: It's earliest records are from around the 12th century. The earliest forms are written in a Latin orthography (though very different from today's). The Latin alphabet also took hold in neighbouring Poland, having been brought there by Christians, or by them that translated early Latin texts, as the first way to record the Polish language.
So the answer to your question is no, not all Slavic people used the Cyrillic alphabet.
Is the reason why some of them displaced the Cyrillic script the fact that the it was connected to Orthodox Christianity while they were/are mostly Catholics?
Not (quite) so. At least in the Lechitic, Bohemian, Moravian areas, Catholicism did not displace Orthodoxy, it displaced some kind of Paganism. Catholicism, having Latin as a liturgical language, of course brought with it the Latin alphabet.