These totes are reused many, many times considerably reducing the number of plastic bags that get used. The problem with this conclusion, however, is that it doesn't consider the 'birth-to-death' lifecycle of the plastic bag and the tote. In other words, what resources were used and pollution emitted in order to create and deliver those bags?
Quartz journalist Zoe Schlanger summarized the findings of a recent Danish study that examines this very issue:
Cotton bags must be reused thousands of times before they meet the environmental performance of plastic bags—and, the Denmark researchers write, organic cotton is worse than conventional cotton when it comes to overall environmental impact. According to the report, organic cotton bags have to be reused many more times than conventional cotton bags (20,000 versus 7,000 times), based on the assumption that organic cotton has a 30% lower yield rate on average than conventional cotton, and therefore was assumed to require 30% more resources, like water, to grow the same amount.
Even adjusting for the benefits of organic cotton production—like less fertilizer and pesticide use (and therefore less eutrophication and water contamination caused by growing it)—conventional cotton came out on top.
The report also assumed the cotton could not be recycled, since very little infrastructure exists for textile recycling.
With plastic bag bans soaring in popularity globally (127 countries have adopted plastic bag restrictions, and New York City just passed one this week), the question of what will replace plastic bags has become more pressing. We know that single-use anything is a terrible idea, whether it is plastic or not, so replacing plastic bags with paper ones will surely have terrible side-effects like increasing deforestation. Making a paper bag also requires more energy and water than making a plastic bag, so for other environmental considerations besides litter, paper products may be worse than plastic ones.Source
To be honest, I'm not sure what to do with this information. This is the problem with trying to identify the most 'environmentally friendly' products. Almost every product harms the environment in some way, but not all harm it in the same way. The only way to fully understand the impact an item has on the environment is through birth-to-death lifecycle studies, which are much more difficult to implement and measure.