The title fully describes my issue. I've attached a GIF screen recording of my struggle.

I tried increasing Grab Sensitivity and Click/Drag Threshold inside Preferences. These options had noticeable effects, but the guides were unaffected.

If anyone has a fix, workaround, or confirmation that this is an unfixed issue, I'd greatly appreciate it!

What I find can help is go Preferences->Input/Output->Input devices->Grab sensitivity= 20 pixels for instance - requires restart of Inkscape.

Something else to check is that you haven't somehow got 'Lock All Guides' under the edit menu switched on (which is what I did with a template file).

I indeed tried restarting Inkscape after changing all settings. It appears that Grab Sensitivity and Click/Drag Threshold both do not affect guides.

"Lock All Guides" is also not on. I'd certainly hope that this option would truly prevent the guides from being moved, as opposed to merely shrinking the clickable area!

I did some further reading and found that this is an issue dating back over 12 years. Here is an old forum thread below. It appears the contributors to the forum thread could not find a solution either.

https://alpha.inkscape.org/vectors/www.inkscapeforum.com/viewtopicca39-3.html?t=10392