I was searching a lot and could only find dosages for curing cancer and allowed emission, but no Iodine-131 dose that could be connected with increased thyroid cancer risk (like, 10mSv is the radiation dose resulting with measurable increase of cancer).
The Central Laboratory of Radiological Protection publishes Iodine-131 content in air measured in $\mu$Bq/m$^3$.
The number has grown by 3 orders of magnitude since the Fukushima accident, and while I strongly believe it's still good 6 orders of magnitude below dangerous levels, there's no convincing of some people without solid numbers - and finding these has proven quite hard.
So how can I then get either the safe levels of I-131 in air in ($\mu$Bq/m$^3$) , or a way to (indirectly - this gonna be convoluted) convert the content in air ($\mu$Bq/m$^3$) to dose equivalent radiation ($\mu$Sv) from absorbed Iodine?