[turns my jester cap backwards to show i mean business]
Long answer: without reading the book I can't really refute more than what you have said here but let's give this a whirl. I am sure it is a very very fun book series! I honestly am going to not be mean because I don't wanna be a hater about it and its not about accuracy so much as having a good time, yknow? I am sticking with two factors here because we're answering your childhood question: the firearms production and the textiles. These are the two things I can focus on quickly.
Part of the issue with reliable firearms is that they are dangerous. We know guns are dangerous, this is nothing new. I can't really summarize 800 years of history that quickly but one of the main issues with mass production is quality control. You would need to refine a large amount of metals, build firearms to spec, and train a defense force on safely using them, and wikipedia says the guy had only 10 years to do it.
The textiles, I am of course far more qualified to say that he would have been laughed the fuck out of the region for trying to introduce t-shirts. There is in particular this... 20th century idea among the general populace that modern clothes were the Most Comfortable things in the world, esp once we really relax dress codes after the late 1970s onwards, which is when this series was written (started in the 1980s it seems). Industrialization made clothing cheap, not better. Again extremely broad strokes being applied here but historically having extremely good fabric for your clothes was how you showed off your wealth, not the cut of the clothes alone, especially when styles changed on a far slower basis than today's trends. Trends and fads absolutely happened, and clothing would be taken apart and refashioned, often over decades. T-shirts started off as underwear in the late 1800s. It slowly evolved into its own thing to be worn, as part of a younger countercultural movement over decades and working class style, especially with laborers and former military who continued to wear it after having been accustomed to being issued t-shirts as part of their uniforms. We're so far removed from it today that most people don't know that it started off as underwear.
I'm of the opinion that 13th century Polish people would see one single layer of clothing like a knit t-shirt for what it is intended originally to be: as the bottommost layer, the underwear. And they would see it as poor quality, nonsensical, ugly, and cheap underwear at that, that fails to stay sanitary and is harder to clean than tabby woven linen, which you can safely beat with a fucking rock in boiling water with caustic soaps when wet to scour it and then lay on grass to dry to activate properties to bleach it white. Having hard-wearing underwear that you can boil and beat and bleach helps you stay clean, and changing that out often and not the expensive outermost layers that everyone sees means you can be nicer to the stuff that has the expensive dyes and embroidery and heavier materials like wool or furs that are just harder to wash, physically.
This is all extremely flippant and un-nuanced but when you have a whole culture around cleanliness that your very clothing choices reinforce and require for participation in society, why on fucking earth would someone grab a t-shirt over plain woven linen. Especially when historical clothing was by and large pretty damn comfortable.
