Hmm. I note that there is a "Refactor Fields" tool in an available GIS toolset that might be employed in a Rube Goldberg-inspired workflow to change field orders in geospatial data tables. Might be worth a look.
I stopped trying to do this. Now, I write a single spatial SQL query to PostGIS and visualise in QGIS. I get the attributes that I want in one step. I can export to share back to ArcGIS Pro users
I think it would be incredibly helpful to be able to permanently reorder fields in a table. Right now, I use the X-Ray add-in for ArcCatalog to reorder fields. It has problems, such as dropping subtypes, but is currently the easiest method I have come across. The add-in includes a reororder fields tool. See links below:
We've been discussing/arguing about not having this feature at least since Esri adopted python in 2005. It's been almost 15 years! If it hasn't happened by now, pretty sure it's not going to happen!! I think it's funny(?) that this thread is tagged "Under Consideration". This thread is 9 years old!