The problem is that most normal people (HN is not normal - mostly for the better) don't even understand what sideloading is - let alone actually care.
How can we fix this?
(aside from making people care - apathy enables so many political problems in the current age, but it's such a huge problem that this definitely isn't going to be the impetus to fix it)
Calling it "sideloading" instead of "installing" software successfully cements the notion that it is somehow not a completely normal thing to do. That's problem solved for the Googles and Apples of the world.
See the history of "jaywalking".
There is no choice of words that will make it normal to install mobile apps from anywhere other than an app store. Whatever word we use will take on the meaning of doing something unusual.
"Sideloading" doesn't have an inherent or deeply ingrained negative connotation. I don't see a reason to try to change it.