Luts intensity slider greyed out

In the Basic tab, the Input LUT slot doesn't have any "intensity" control. That "Intensity" slider is below the Auto color correction button, right? So that is only controllling the amount of the correction the Auto color button has set. So you hit the Auto color button, you can either accept the 'level' it appllies, or use the Intensity control to change the amount.

(Note, the control is below the Auto Color button, right? Think ... processing order ... top to bottom. )

The Creative Tab's LUT slot does have that Intensity slider right below it. Which applies to the control immediately above it, that LUT slot.

The UI design is actually 'clear' between the two tabs, after you look at it a bit. And a bit of free advice ...

LUTs are incredibly capable, and ... at times, incredibly destructive. I work for/with/teach pro colorists. A common comment is that "A LUT is the dumbest math out there." And even the fancy 3D ones, which actually embed one LUT over another sort of, are still "dumb math". There's no "if this then that, else ... if that, then this" computational power to them.

Which is why say for normalization of log encoded media to linear, many colorists vastly prefer algorithmic based tonemapping (which does allow for amazing complexity of options) or, only in Resolve of course, DCTL's.

Most colorists prefer to only use LUTs where they know precisely what that LUT does because they've tested it with test clips, and often, have even tried to re-create it. I've heard one noted colorist say, essentially, that:

"If you haven't pushed a LUT hard enough to have intentionally broken it, you don't know when, why, or how it's gonna mangle your grade. Don't be dumber than a LUT ... it's not a good Look."