in my use at least Mojo 1 and 2 are the same for this issue.
In my experience what you've described isn't the issue, .....if it was the Mojo would never
have been successful as it would have been recognized as a defective product.
What caused the white noise for me - and was never
deafening as I don't listen at a loud level - was the micro USB connector getting dislodged/losing contact.
This is based on using Mojo 1 for five years, and Mojo 2 for 7 weeks. Of course there
may be another/other reasons but this has been my experience.
Changing the rate never caused the white noise for me.
Once I was careful not to move the Mojo while in use, all was well. In IOS
the track sample rate changes automatically, Mac OS currently doesn't.
I'm now using Mojo 2 and sometimes Mojo 1 with my iPad Pro.
IOS does support auto-rate switching, however the Mac doesn't....
in order for higher rate tracks to play at that rate it can be changed manually in Audio Midi Setup,
otherwise it will be resampled at the rate in AMS. This is the same for Amazon Music,
the only service that I've used that auto changes the track's rate on Mac is Tidal,
which I no longer use to due to price.
Now that I've explained the above, I'm hoping you'll find as much listening joy with Mojo 2 as I'm
experiencing as are many others here. When partnered well it can produce
absolute magic, it's very special IMO. Your use and your ears will tell if it's right for you.