There are a lot of shoes out nowdays that have the insole NOT glued down, so it is easy to take it out or change it over for an aftermarket one, including putting in the orthotics variety, of which there are quite a few - Footprint, Remind, Etcetera and others.
Being able to try on shoes is a big plus, as well as look and and check out the insoles but some places will not have them or will only be accessible online.
My feet have all sorts of issues, but I do things to my standard and pro Vans (which are one of the thinnest and softest shoe brands on the market) to make them way more stable including cutting cardboard and gluing it down the inside to increase arch support under my custom insoles, but there are products you can buy ready to go.
The most frustrating thing I find is shop staff will often recommend what they only have in stock or what they only find works for them, which may not work for you or other people, so just check things out or try them on if possible.