We leave later today for Munich, arriving there 6PM local time tomorrow. Tuesday we are planning HOHO bus. Prediction is 90% for rain on Wednesday. Our plans had been to do a Grayline castle tour that day, and I'm thinking that is still a good idea because it sounds better than tramping through town in the rain. Thursday is our last day in Munich, and we'll just suck it up and hope that 50% chance of rain leans towards 50% NOT, at least by the end of the day. Any reason not to do the castle tour in the rain?
Not as long as you have an umbrella. Although Hohenschwangau is a relatively short walk from the ticket kiosk, it takes about 40 min (plus or minus) up a long trail to get to Neuschwanstein. If you take a horse carriage up to Neuschwanstein, they do have covered tops for the rain, but you still have to walk from the kiosk up to the carriages outside Hotel Müller, and there is another short walk from where the carriages turn around up to the castle entrance.
I think I would be more inclined to do the Munich HOHO in the rain than the castles.
Unlike Linderhof, there aren't really an gardens or grounds to explore at Schwangau, so there's no reason rain should stop you. Plus, rain storms in Germany don't tend to last very long, and usually it comes down lightly. Of course, you could experience continued periods of short, light showers throughout the day, but even this shouldn't prevent you from enjoying the castles. At worst, you won't get a good look at the surrounding mountains.