The form is automatically filled in. The entries are not recognized by the server unless I type them. I used to be a Visual Studio programmer and I think there is an html field type for entered fields so the browser recognizes that data was typed into the field. Perhaps the form fill feature in Firefox doesn't set this or the server doesn't recognize it. I doubt it's the former since this doesn't happen on all web sites. Edge doesn't have this problem with their form fill. Maybe the page doesn't have proper settings for Firefox. I suspect this may be the problem?

This could be a method of thwarting scripted account cracking. My guess would be similar to yours, that user interaction causes the text inputs to be fed into hidden fields that are used for the actual login. But why Edge is able to fool the site and Firefox isn't, is a really good question.

Can you post a link to a publicly accessible page (i.e. no authentication or signing on required)?

Not sure how a publicly accessible page will solve the problem? But here you go: https://forecast.weather.gov/MapClick.php?lat=42.166&lon=-87.9571#.YtwAkYTMJhE