Here's a method which I think seems to work system-wide and kills red underlining, overriding the way many apps annoyingly default back to "Check Spelling While Typing".
1. Open "Language & Text" in System Preferences
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2. Under the "Text" tab, select Spelling... (which is probably set to "Automatic" by default), and scroll down to the bottom where it says Set Up...
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3. in the box that comes up, uncheck every language. It seems to require that at least ONE remain checked, though, so I just left "Polski" (Polish?) checked. I don't think it matters at all which one you leave check as long as the English ones are unchecked? Anyway, I left Polish checked and this all is working great.
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4. Click Done to apply the settings, and that main Text tab, leave Spelling set to "Automatic by language"
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Once you do this, from what I can tell you can type anywhere in any app, even with Check Spelling While Typing set to on, and the red underlines won't appear. This is working for me, anyhow. I can type some gibberish like "lkjsfdkljhf" and it will not be underlined. If I go back in and check those language boxes again, type the same gibberish, it will come up underlined in the same app.