I can't be considered an "expert" on iris scanners and their effect on your eyes, but I have been using one of the first commercial phones to implement a successful iris scanner (the Microsoft Lumia 950 XL) for a long while and I can safely and confidently tell you of my experiences.
First off, the iris scanner does not implement lasers of any kind. The iris scanner uses a combination of your front facing camera and an infrared LED in order to better pick out details in multiple lighting conditions (this LED is why the iris scanner still works in almost all lighting conditions except for the most extreme-more on that later). The "risk" here is no greater than walking outside on a particularly sunny day, and in fact is even less extreme in my opinion (given my experiences). You see, sunlight actually typically contains more infrared light than the LED in the phone transmits, which is exactly why the iris scanner typically fails in direct sunlight (because the infrared light present in sunlight completely masks the infrared light in the LED and makes it impossible for it to see you). It's no more dangerous than staring at, well, your lighted phone screen. Especially considering the average duration that the infrared LED light remains on.
This infrared LED is exactly why iris scanners are so secure, and how they can work in near pitch darkness with little to no complications. In most situations, finger print sensors (it's not a scanner) are quicker, this is true, but iris scanners can actually be more secure despite their slightly more fiddly nature. Their safety has been tested for a long time, and I don't see why their implementation in smartphones should make any difference here. These are not retina scanners, and your eye is not an inch away from the sensor.
In my honest opinion, I would not trust the contents of the article linked in the original post, considering it's less than credible sources and the simple fact that people often experience "eye discomfort" when using lighted screens for long periods of time due to the strain that occurs from focusing on these displays. I get more eye discomfort from watching Netflix for long periods of time then from unlocking my phone, even if it's repeatedly over a short period of time. If one is truly worried about the safety of their eyes, I suggest you stop using smartphones and other technology products featuring lighted displays altogether, as the threat is about the same.