There appears to be at least some suggestions otherwise...
Correlation between pubic hair grooming and STIs: results from a nationally representative probability sample
From the summary, they did adjust for age and lifetime sexual partners, but without knowing the details of that hard to say if this is a good example of "correlation does not equal causation" or not since there are other factors (frequency of condom use, hair removal method, etc.) that don't appear to have been taken into account.
Now having said that, I think it's pretty much proven fact that cut/abraded skin is more susceptible to infection, so there's probably something to it. It's just a matter of how much of a risk factor it is, and as we have frequently discussed here, risk is one of those personal things that you just have to evaluate for yourself. I think how much of a factor probably depends too - sex one hour after shaving probably carries a higher risk of transmission than sex three days after shaving. Study seems to back that up with the results for "extreme groomers", "high frequency groomers", etc.