This only affects the home button. If you replace the screen and keep your original home button, there is no issue.
I co-own a repair shop. We have known about this for a while. We won't replace home buttons for this reason. But we replace hundreds of screens a month with no issues.
Apologies if this sounds rude, because that's not the intent. How can you be sure that people whose screens you've replaced don't then get an "error 53" when they later come to do a software upgrade? Because that's the only time it shows up. Would they know to come back to you about it (possibly shaking fist)?
Sorry for the late response--I just now saw this. We've fixed thousands of screens at this point--we'd have an angry mob if screen replacements caused the issue!
Yes, we have had people come back with Error 53; that's how we knew it existed a while ago. All of them had either had their home button replaced or water damaged. We were able to successfully recover one of them after the Apple Store told the guy there was nothing they could do. It was a water damaged home button and we were able to clean the corrosion off of it by soaking it overnight in a special solution. It came back the next day. If your original home button stops working, though, you are screwed.
I co-own a repair shop. We have known about this for a while. We won't replace home buttons for this reason. But we replace hundreds of screens a month with no issues.