Because nothing about seeing Jesus implies that one should not be a Jew. If it worked that way, Jesus wouldn't have been crucified. And from a South Park-specific perspective, why would Kyle seeing the weak, ineffectual person that Jesus is portrayed as convince him that he is the Messiah?
Finally, the term 'Jew' can have several meanings, including that one is ethnically Jewish. Kyle is most likely ethnically Jewish like Matt Stone. He would not stop being 'a Jew' even if he converted to Christianity.