This honestly sounds like a classic situation where people don't understand technology, are scared of technology or a combination of both. Here's an example you could use to possibly explain it to your mother. I have peoples birthdays saved in my google calendar to remind me. I'm sure in the past your mother noted loved ones birthdays on a physical calendar. How could one be bad while the other be okay when they are both literally the same thing?

Here's another example you could use to explain it to your girlfriend. If you wrote your girlfriend a love letter the night before then handed it to her in person the next day, she would absolutely love it! But... you wrote it the night before right? Just like the text right? So why is one bad but the other good? They are literally the same thing but one upsets her and the other doesn't?

Hopefully that helps open their eyes because their logic on how it's a "facade" makes LITERALLY NO SENSE. You are STILL putting in the same amount of effort regardless of if you wrote the text in the moment or the evening before. You could also try and ask them to explain their logic on why it's a "facade" to them. Maybe start off with that before giving them the examples?

NTA in the slightest. Your brother definitely is though and I reckon the way he explained it to them is probably what made this situation look bad when it's actually a non issue! Therefore, I wouldn't bother to hold it against your mother and your girlfriend if they come to understand the situation after you explain it to them.