That depends on two major factors: what region are you talking about, and what documentation existed of a particular individual being ethnically Jewish? Different axis members contributed to the holocaust to different degrees, a notable example being Bulgaria who was willing to not deport "their" Jews but in regions that they occupied outside of their pre-war borders they contributed to the rounding up and deportation of Jews, as mandated by the nazis. But more important is what documentation there existed of an individual being ethnically Jewish. Despite most European antisemitism having been based on religious hatred and prejudice, the nazis reformed that and focused rather on the ethnic significance of being a jew (this can be chalked up to a multitude of factors, not the smallest of which was that many prominent communists, such as Marx himself, were jews). Therefore, the nazis did not limit their persecution to religious jewry, but rather, to ethnic jewry. So if records existed that showed that an individual was ethnically Jewish, and these records were accessed by the authority conducting the final solution related operations in the given area, then the individual would likely be killed or deported. The nazis also standardized certain physical metrics to measure whether someone was a jew if there were doubts about their racial "purity", including certain measurements of nose size. This makes the answer to the original question simple: regardless of religion, anyone that could be proven to be an ethnic jew would be persecuted without any regard for religious identity. This however may be an incomplete answer so any corrections or added information about how the persecution of Jews was conducted in various axis states is welcome.