I guess both views have validity. So maybe we should relax a bit.
Looking at the total amount of plastics in use the bags are surely neglible.
And having a mindset not to produce unneccessary waste is also ok.
In my opinion the point is to use plastics when it is reasonable and to avoid them when it is not reasonable. It is quite that simple.
Besides that, the topic is more complex - as always - than it seems.
Where does the plastic end up? What kind of plastic is the bag made of? Is it reusable or being burned to generate heat? Do people re-use/dispose of properly? Or does it end up in your garden? How long does it serve it’s purpose (one of the main criticisms of plastic bag use)? How to judge environmental impact - by weight, volume or surface area of the plastics? Etc.
And guess what, I have a degree in plastic engineering and I nevertheless prefer reusable bags made of textile. They can hold more weight more securely and simply have more style. But, I also have some plastic bags, because sometimes they are more suitable.