There is a connection. Fundamental Christians tend to deny human mediated climate change and they think vaccinations and genetically modified foods are dangerous. I don't have the time right now to dig up a bunch of sources, just do a google search for Christians and any of those terms and you will see the connection.
I'm fairly sure that vaccine opposition does not correlate with religiosity. I'm sure I've seen research showing this, but haven't been able to find it in a quick search - I'll come back if I do. A quick Google search as you recommend, however, finds only sources demonstrating no correlation between political views and anti-vaccination beliefs; despite known correlations between political beliefs and religious views.
If there's a correlation between climate-change denial and religiosity I suspect that's more an artefact of the fact that conservatives are more likely to be Christians (in the US) - climate-change denial tends to be caused more by fear of governmental regulation (in my opinion).
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