After Jesus proclaimed boldly about His link with the Father and rivers of living water, some believed that Jesus is the Prophet or Christ (7:40-41). Others doubted because they thought Jesus came from Galilee rather than Bethlehem (7:42). Note that Jesus was born in Bethlehem and grew up in Galilee, however ("coming" in some instances means "born" but other instances does not).
Struggling with Bible "contradictions" isn't a new problem -- even people at Bible times struggle with "contradictions"! However, even though there may appear to be "contradictions", there are still many people who believe in Jesus. The believers know why the "contradictions" aren't really contradictions (AKA does not violate the Law of Contradiction) -- one example being the above explanation for Jesus "coming" from Galilee rather than Bethlehem. In the midst of struggling with Bible "contradictions", we can examine deeply.
Anyway, because some people believed and others disbelieved, the Judeans pretty much split themselves. Of the people who disbelieved, they wanted to capture him but at that time were unable to.