Train travel from Munich airport to Fussen

If you are referring to the possibility of a strike, who knows? Stay informed with the news. The contract has not been settled yet, as far as I know. The last one was coordinated with a school holiday period for maximum effect. If no holidays in this period, it could pass without incident. I am not familiar with bus service to Fuessen. There is bus service from the airport to central Munich. There will be some chatter if a strike is imminent.

I'm not sure about all the way from the airport to Füssen on a strike day and arrive early enough to see the castles, but there are options.

Many (most?) of the "3rd party" castle tours use the trains, so ones like Mike's Bikes will probably not be operating, but Greyline uses their own buses, so they should be operating. However, these 3rd party tours are expensive. They go from downtown Munich to Füssen. The Greyline tour leaves downtown at 8:30, so you probably don't have time to get in from the airport and catch it.

Buses of the MVV (Munich metro) will be running as will ALX trains. ALX is a privatized line, and their trains were running during the last strike. There are ALX trains from Freising to Munich Hbf every two hours at 8:48, 10:50 etc. You can get from the airport to the Freising Bhf on an MVV bus that runs every 20 minutes. The trip takes about 20 minutes.

ALX also runs trains from the Munich Hbf to Kempten, and there are buses from Kempten to Füssen. There is an ALX train leaving Munich Hbf at 7:20, arriving in Kempten at 8:48 and a bus leaving Kempten at 9:10, getting to Füssen at 10:30. However, the next bus leaves Kempten at 12:05 and gets to Füssen at 13:50, cutting it a little close if you want to see one or both castles that day. There is also a later bus getting to Füssen a bit before 4 PM. That would probably work if you were comiing from the airport, staying overnight in Füssen, and seeing the castles the next morning.