Is there some way to subscribe to an internet calendar on Android without logging into Google calendar and adding it there?
This is not possible in normal way, but can be done with a bit tricky.
You can visits https://calendar.google.com/calendar/r/settings -> Left panel -> "Add calendar" -> "Browse calendars of interest" -> "Regional holiday" -> Select and Tick "Holidays in specific country" -> It will add to left panel under section "Settings for other calendars" -> Click it -> "Integrate calendar":
There are two methods:
The "Public URL" can be direct open in Android web browser and use its "Add to Home screen" option to make a shortcut on screen. The advantage is you can always get the latest date, but you can't get event notification.
The "Public address in iCal format" can be open in Android web browser and download as .ics file. Before open .ics file, ensure delete the cache/data storage of system app called "Calendar Storage" in app settings first (Need to choose "shows system app/processes" to see that app). And you may also need to navigate in "Accounts" -> "Google" -> All Gmail -> turn off Calendar sync. After open the file with "Google Calendar" app, it by default will reside "Phone" OR "Holidays" category. Choose "ADD ALL" to add all events to calendar. Finally relaunch the calendar app, you should able to see the latest events added by .ics file up to next one year. If it doesn't showing, swipe the left panel and tick "Phone"(Huawei P9 Lite) OR "Holidays"(LG Nexus 5X) to shows. Note that upper right "refresh" option can toggle back Gmail events, it's up to you. The disavantage of this method is its event is fixed on .ics file and will not up to date without re-download and re-add. And I noticed I must clear "Calendar Storage" data cache (Gmail events) first or else it will popup a toast about incomplete to add all events. One thing you should know is the events timeline in Google Calendar app actually saved inside "Calendar Storage" system app data cache which can share to other app, not its data cache.