Even in German, mixing up o and ö or u and ü is still a spelling error. They sound very different, even if they are in some formal sense the same letter.
The real question is how Germans spell in contexts where it's not easy to add those diacritical marks. Do they omit them, or take the extra effort to put them in / replace them with some digraphs?
My own language has several diacrititics that completely change the pronunciation (ă for schwa, â and î for a vowel that has no equivalent in English, ș for sh, ț for the zz from pizza), and is otherwise very phonetically written. Still, when writing in informal contexts on English keyboards, people generally just use a/i/s/t and rely on context to make it clear which word is meant. In old SMS writing, they would sometimes use sh and tz, but still a/i. So even though the diacritics fundamentally change pronunciation, and make a few words indistinguishable, they are not critical to the understanding of a text and local readers don't fully require them.
From what I've observed, if they only get ASCII they write out the diacritics phonetically. As an example, https://en.wikipedia.org/wiki/Chris_Huelsbeck interchangably uses Hülsbeck and Huelsbeck, but never Hulsbeck
