I developed the Instagram Web Data Connector that you mentioned. This WDC doesn't store any personal data and doesn't access any data. After all the WDC are different, it depends on the developer and their code.
I hope it helps,
I would like to know how safe it is to use open/free WDC for creating viz. on data based on Twitter, Instagram or Facebook?
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These WDCs are created by people from our community, Tableau doesn't support them.
If you want to get a look closer to the code itself the code for these 3 WDCs are available on the community