I think when people talk about break in oil, they are just talking about regular oil, not synthetic.
Supposedly it allows a little more friction in the beginning to help all the parts seat. Plus, you'll have to change the oil pretty quickly too, and no need wasting money on synthetic for oil you'll only use for a little while.
After the initial break in, some people will run regular oil a second time, and others will switch right over to synthetic. They state the reason for the second run of regular is just to make sure you get all the break in stuff out.
I've been running the Suzuki oil in my KQ since I got it. No real reason though other than personal preference.
I've had several ATVs prior, as well as dirt bikes, and I always used regular Valvoline 10w40 in them. You just have to look on the bottle and make sure that it does NOT say energy conserving. The energy conserving oil has additives that can cause the clutches to slip. I never had a problem in the tens of thousands of miles I put on my other ATVs and Bikes using regular oil instead of motorcycle oil.
Here is a picture of the API ratings you find on motor oil. You see how some have "energy conserving" around the bottom of the circle, and how others don't. You want to make sure that you get the ones that are NOT energy conserving, and also the right weight and rating as recommended by the ATV manufacturer: