This is simplified, but in general the magnetic field falls off in strength inversely to the cube of the distance from the magnet (green line below).
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The majority of headphone drivers have a magnetic field strength on the order of magnitude of milliTesla (~30mT or less), which means that by 2 millimeters away the field strength is already ~88% weaker, 3mm would be ~96% weaker, 4mm ~98% weaker, 5mm ~99% weaker. I expect the headphones on your head would be at least a few hundred millimeters away from the CRT, so there's very little risk of noticeable interference. Now, with field strength on the order of magnitude of Teslas (>1000mT), which very high-end headphones or speakers systems would have, it would take 2 meters of distance to reduce the field by 88%, 3 meters would be 96% weaker, etc. This is significantly more distance but the rate of fall off is still dramatic.
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If you notice that something starts affecting the colors on the monitor, just move it away and there's usually no harm done. You aren't going to damage it by momentarily placing a small magnet near it. It gets more serious with close, prolonged exposures and/or more powerful magnets because they can magnetize or physically warp the iron-alloy mesh that the electron beam is fired through, causing it to hit the incorrect phosphors on the screen. Power cycling or manually degaussing the monitor can usually solve small mesh magnetization issues but the warping is most likely permanent damage.
I also saw your related post about the Altec Lansing speakers. The satellites probably also have magnetic field strength on the order of milliTeslas so they only need to be on the order of millimeters away from the monitor. There's probably enough space in between them just due to the speaker enclosure/housing and monitor bezel. Compaq even sold monitors with speakers hanging off them for a while. I had one of these growing up and never noticed any purity issues, but I'd be interested if anyone else did.
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