Currently, there is a known limitation where pop-up field (re)ordering done in Map Viewer (Beta) does not translate to the pop-up when viewing in Field Maps. ESRI's 'solution' is to make pop-up field order changes in Map Viewer Classic. However, saving any changes in Map Viewer Classic will wipe out custom forms created thru the Field Maps WebApp. Therefore, the 'solution' essentially erases your Field Maps forms if you've gone on to configure those after creating the WebMap. I was told - via BUG-000139509 - that this will not be addressed (!).
If you attempt to make other pop-up changes in Map Viewer (Beta) - such as date/time format, alias names, field inclusion/exclusion, etc - these changes do translate to Field Maps when viewing the pop-up but this also will wipe out your custom Field Maps forms.
This functionality paradox has significant workflow ramifications and destroys any flexibility once you've set your original pop-up configuration (and have spent time configuring Field Maps forms thru the Field Maps WebApp). If you wish to add a new field to your dataset (andWebMap), change the alias name of a field, reorder your fields, etc - basically any adjustment to pop-ups - your options are to go ahead with the changes, knowing you'll have to recreate all of your custom Field Maps forms or just do not make any changes. I do not think these are acceptable options. I have run into this paradox numerous times; it would be great to only have to configure a WebMap once but that expectation is not realistic. I have intentionally limited myself with Field Maps because I can't afford to be continuously recreating custom forms whenever my organization inevitably requests changes. I am hoping ESRI will take this significant flexibility/efficiency limitation seriously at some point.
