What would happen if there was someone of Jewish blood who was (for arguments sake) a Catholic? Or a person of European descent who followed Judaism? Were both exterminated or just the ethnic Jews?
Both. Ancestry was the primary selecting factor for persecution. I do not know about converts from Christianity; there were not too many of them to begin with.
A deleted reply to this thread said this:
Blood, descent, ethnicity were just fashionable words used to excuse the good old christian antisemitism.
This is most emphatically false, and constitutes not only a misunderstanding of 19th century racial "science", but also of Christianity and Hitler himself. In fact, the greatest papal complaint about the various anti-Semitic measures which were put in place in Germany under Hitler is that they affected Jews who had converted.
The difference between the Christian and "scientific" approach to the Jews is also well-seated in modern scholarship, where the distinction is drawn between anti-Judaism, an opposition to the religion, and anti-Semitism, the opposition based on "racial" grounds.
Answering the question of who is a Jew was an important question for Hitler's antisemitic policies. Officially a person was considered to be Jewish, and thus be exterminated, if they had one Jewish grandparent, regardless of their current religious affiliation. However, the likelihood of persecution generally decreased with the fewer Jewish relatives one had. This meant that even if you were indeed Catholic but one of your grandparents was Jewish, you could (though it was less likely than for fully Jewish people) find yourself persecuted.
Conversion to Judaism was uncommon until recently - and even know it remains a rarity. Some officials within different sects (as there is no central governing body of Judaism) maintain that it is not possible to convert, or that converts to other sects are not properly Jewish. Conversions of Jews to Christianity or even secular life was much more likely (and actually quite common) in Germany - and they were persecuted by Hitler despite this.
In essence, Hitler's policies were aimed at murdering not just people who were clearly Jewish, but people who were ethnically Jewish (had some clear amount of Jewish heritage). People closely associated with Jews (such as through marriage) were also at risk.
Check out the website of Yad Vashem for more details