Message from Esri Tech support:
Thanks for confirming that my tests replicated the behavior you're seeing. We also had several other tests run, both in ArcGIS Online and in Portal. In each test, we were consistently seeing that New Map Viewer arranges fields alphabetically, in the pop up.
I've since learned this is the intended behavior for pop ups in New Map Viewer.
The Map Viewer offers a lot of new capabilities but there are some differences between the two. For instance the analysis tab is not available in new Map Viewer but it is in old. Another example is the "save layer" button used to be just for the old map viewer but now it is also offered in the new. In some cases, the new map viewer is still catching up to the old map viewer, in terms of capabilities and functionality.
As a workaround, you may decide to stay with Map Viewer Classic, particularly when configuring pop ups and working with forms (e.g., for use in Field Maps, etc.).
Let me know if you have additional questions or if we should explore other workarounds while New Map Viewer plays "catch up," in this instance.
Thanks for the follow up and also for providing feedback on the New Map Viewer and our latest release. Our release team has been hard at work, addressing potential issues that are arising during this early stage following the release. I'll provide your feedback to the development team, so that we can keep aligned with customer concerns and needs going forward. Development is a continuous process, and we're constantly adapting and changing to flow with the needs of the customer, as closely as possible.
To that end, I would also encourage your participation in the Ideas forum within Esri Community. You may already be participating, in which case, thank you very much for taking the time to contribute to the conversation. Ideas submitted there are monitored, voted on by other community members, and many are implemented by development for future releases across all Esri products and solutions.