I've updated demo.sogo.nu. Can you still reproduce the problem? Make sure to empty your browser's cache.

I see no change on demo.sogo.nu, problem is still there.
I cleared cache, I used new account, I used firefox and chromium on linux and firefox on win10.

I can't reproduce the issue.

Today I asked for test my friend. He uses MacOS and he never visited demo.sogo.nu yet.
He confirmed the problem on your site.
Now I see following behaviour:
I go to Calendar module, Month view, click mouse on some day and move with mouse. Form is opened, "All day Event" is checked. "Title" line is red. I write something, color changes to white.
"To date" line is set to selected day (it is same as "From date") and is red. SAVE button is unselectabled.
I click on "To date", calendar is opened. I confirm that same selected day.
"To date" line goes to grey color.
I click on "To date" again and confirm that same selected day again.
"To date" line goes to red color again.

For Info:
I had that too.
I then had to use <Return> once instead of clicking on the greyed out "save" button.
It stored the event with that.
All subsequent creations worked without that problem.

Where exactly did you use <Return>? It does nothing for me.

I have the same problem on my own instance and can reproduce it on demo.sogo.nu
The prefilled end date value cannot be used and has to be changed to a different value and back in order to be able to save the calendar entry.

Same problem here. If I create an all day event in the monthly view by dragging the mouse, the event can only be saved if the end date is changed to a different value and back. Events that span multiple days can be saved immediately. The date format doesn't matter. I can reproduce this problem with DD.MM.YYYY and YYYY-MM-DD.

Please temporarily modify UIxAppointmentEditorTemplate.wox with this patch:

diff --git a/UI/Templates/SchedulerUI/UIxAppointmentEditorTemplate.wox b/UI/Templates/SchedulerUI/UIxAppointmentEditorTemplate.wox
index bb822978d..db4982a28 100644
--- a/UI/Templates/SchedulerUI/UIxAppointmentEditorTemplate.wox
+++ b/UI/Templates/SchedulerUI/UIxAppointmentEditorTemplate.wox
@@ -159,7 +159,7 @@
           <div layout="row">
             <div flex="50">
               <div class="pseudo-input-container">
-                <label class="pseudo-input-label"><var:string label:value="From"/></label>
+                <label class="pseudo-input-label"><var:string label:value="From"/> {{ editor.component.start }}</label>
               </div>
               <div layout="row" layout-align="start end" layout-wrap="layout-wrap">
                 <md-datepicker ng-model="editor.component.start"
@@ -174,7 +174,7 @@
             </div>
             <div flex="50">
               <div class="pseudo-input-container">
-                <label class="pseudo-input-label"><var:string label:value="To"/></label>
+                <label class="pseudo-input-label"><var:string label:value="To"/> {{ editor.component.end }}</label>
               </div>
               <div layout="row" layout-align="start end" layout-wrap="layout-wrap">
                 <md-datepicker ng-model="editor.component.end"

Show me screenshot of the appointment editor when the end date is invalid.

Here's a screenshot of an all-day event in German and timezone CEST.

all_day_event.png (22,430 bytes)   

all_day_event.png (22,430 bytes)   

It seems that this problem is related to the timezone. I can reproduce the problem on demo.sogo.nu if the timezone is set to CEST.
If the web browser is started from the command line with "env TZ=EST firefox", I can save all-day events on both demo.sogo.nu and my instance.

See issue #11963 of ng-material. Let's wait for release 1.1.25 or 1.2.1.

1.1.25 was released 2020-08-31 with a fix for #11963 :

https://github.com/angular/material/blob/master/CHANGELOG.md