Your issue probably has nothing to do with loiter at all.
There is some abnormalities in your log and serenely some issues that has to be sorted out.
The first issue and probably the most serious is the vibration issue. You have high vibration in the pitch axis and extremally high on the roll and yaw peaking at 80. (below 30 usualy works, below 10 is good. Over 30 and it will most likely have an effect on flight performance.
The oscillations looks to be the roll axis. The rate controller gain also oscillates greatly resulting in oscillations in flight. You mentioned you didn’t see any of this in alt.hold. I have seen this in many times before and for loiter modes to work, the tune, not only the PIDs but filters and other values must be good in order for loiter to work.
In loiter the flight controller uses many sensors and a lot of data using and EKF to control the aircraft. The EKF hates vibrations and needs well tuned filters and values to work properly. This is probably why you only see the issue in loiter. It’s still there in alt.hold but not visually detectable.
The oscillation in the rate controller probably contributes a bit to vibrations and increases noise in the aircraft but there is differently a vibrations issue here. I have dealt with this before and it’s unfortunately a hardware problem. This much vibrations can’t be handled by changing parameters.
Youre aircraft is also quite light in relations to your motor system. It hovers at around 1250 pwm (1000-2000). A hover output of around 1500 is about where the limit is, and also where many drones fly at. This is not an issue, although with the high vibrations and the rate controller oscillations the motor outputs also oscillates at hover. Since your copter is quite light, the outputs hit their lowest value which limits the copters ability to maintain control. This would be the same it it was too heavy and the output would hit max value.
Although your light weight should not be an issue and the motors hitting lowest value a lot would be caused by the other underlying issues.
So, you probably have to lower your PID values a bit for roll, but before that the vibrations needs to be fixed.
Have you set up the notch filter? that is extremally important on the later firmware’s. The filter handles noise which can cause a lot of issues. Reducing vibrations and noise is key to getting a good tune! So first you need to address your hardware to find sources of vibration.
Could you post some pictures of the setup so that we can see how everything is mounted etc?