Americans are generally very tolerant and patient with non-native speakers butchering proper english. So no, it's not nearly as grating to an American to hear people mispronounce english words than it might be for Germans.
It just bothers the historical linguistics nerd in me that all the other Germanic languages (other than Icelandic) lost the beautiful Thorn and Edh sounds consonants :-)
I've always found it interesting that the German approximation is "z" here when it could be "t" or "d", since that is what "th" sounds turned into in Old Franconian.
I am not sure why there should be an emotional factor here, as expecting everybody to conform to some pronunciation ideal they have no experience with is arrogant, to say the least.
But see, that's the point. We're not speaking German when we use a borrowed word in English. It's no longer a purely German word, despite its origins, just as "xylophone" isn't a mispronounced Greek word, nor "Handy" a misused and miscapitalized English word.
That's not hubris, it's just descriptivism.
"Wagen" on its own would probably be pronounced like way-gen, if my english intuition is not fooling me. Instead it is pronounced like wuh-gen.
I don't really care about this either way but if you are bothered by something the weird mixture is.. a bit annoying.
This same goes for English speakers too. I know how Volkswagen is supposed to be pronounced (I know some German) but that's not the way English speakers would say it.
I don't think there is anything to be bothered by any of this. This just adds to our diversity.
Nope.
And yet, English has an "f" sound. German has an extremely consistent spelling and essentially all "v"s are pronounced as "f". We share (the latin) alphabet, and English has absolutely no authority, given how inconsistent it is.
Given that, I will say the voiced "V" when speaking English and the unvoiced, as necessary, speaking German.