The 74LVC1GU04 is an unbuffered inverter, which (according to the datasheet) is intended to be used in linear mode in applications, such as crystal oscillators and linear amplifiers with negative feedback.
But the same datasheet claims that there is a "Schmitt-trigger action" on the input. That is the standard formula meaning there is a small (100 mV) hysteresis on the inputs. All CMOS families use such inputs nowadays.
But even a small hysteresis on the input will definitely make it impossible to use the element in linear mode with negative feedback - it will simply oscillate.
Does the 74LVC1GU04 really have a "Schmitt-trigger action" input? Or is there a mistake in the datasheet and does especially this element have input without hysteresis?