I think there is a sweet spot.
Too "modern" and I assume a site is using excessive amounts of tracking and playing other tricks with A/B testing different marketing tactics for services to try to milk their customers for all their worth.
Too crappy and I start to question if the site is actually secure and if they are putting enough money into IT... or if it's even the real site vs some kind of scam.
Both can be problems that erode trust, but they are different problems.