They didn't figure out anyone's ethnicity, according to their press statement they banned all accounts which were accessed via Iranian IP's. While seemingly a little heavy handed IMO, they are trying to comply with US laws. They also provided a way for people to send an email to address their specific accounts if they feel they were terminated improperly.

Slack is protecting their multi-billion dollar business and their investors which are both based in the U.S. If they do not, they could run into trouble and put far more at risk. This does not only affect Iran, it affects other countries too which the U.S. has active sanctions against.