Debunking weather conspiracy with statistics - why does temperature rise then fall for last weekend in June in recent years
You are asking the wrong question. The real question is why some podunk single city festival and not other larger more costly events, like space launches, national holidays, military campaigns, hurricanes, or a million other festivals. The conspiracy theorists likely picked that festival through data dredging, which means you are not going to disprove it by looking at the same data. If you compare enough festivals you will find some in which the weather does weird things, it is the law of large numbers in action.  

A festival that started in the 1970's is perfect for data dredging, there is a change in the underlying forces of weather in the 1970's. The undeniable warming trend in global climate starts around the 1970's so if you divide your data sets before and after any point around that time the data will always show a significant difference, unless you correct for that shift. Without correcting for it all you are detecting is climate change, a known factor,n anthropomorphic factor at that. So really humans are altering the weather, just not in the way your friend thinks.