"Are some environments or countries more or less tolerant of grungy bike tourists in potentially dressy locations?"
My experience is that in Germany folks are very accustomed to sport clothing. Hiking is very embedded in German culture, and biking and nordic walking are also common today. I'd have no concerns at all entering any 'tourist' destinations in bike gear. For some restaurants, and events like opera, it would be best to clean up a bit, but you're less likely to run into that during a day's ride.
The Netherlands and the UK would also be places where I've felt little pressure to dress up.
Belgium, especially Brussels, tends towards the dressier side. Italy is the place I've felt most inclined to want to present my best appearance.
A few things that I've adopted for European touring that might translate to any other place where you want to blend in:
--Keen leather bike shoes... they take SPD clips, are very comfortable for all day riding, and look like dress shoes.
--Monochrome bike shirts, especially the newer non-scratchy wool variety. I've been astonished at how non-stinky wool is, and the range of temperature it's comfortable in.
--For a quick cover up, dark rain pants over bike short work well.
--Even in the U.S., I always make a point of taking off my bike sunglasses before entering any business. That seems like simple politeness to me.
Hope this is useful. Happy touring!