Babs, remember that for people who play in a drone style, the only string they have to think about is the melody string, so new tunings really mean that the key note (or home note or tonic) is in a different place on that melody string. Obviously, in that style of playing, switching tunings is wholly different than it is for those of us who play cross string and with chords. In my playing, for example, I never think of a note in isolation; I think of chord positions and see the melody out of those positions.
I play other instruments, too, such as the guitar and mandolin. I have no trouble switching from one to the other even though they are tuned completely differently and chord shapes are completely different. I think something similar is at hand for those people who are proficient playing in many different tunings. They simply learn different places to find notes on the fretboard. Their brains flip a switch when they switch tunings in the same way that I flip from guitar to mandolin.
I have not gotten there, I must admit. I almost always tune 1-5-8 and after 5 years I find I am still getting to know the fretboard. (Only a couple of weeks ago, for example, did I find the 8-6+-5 E chord!) This limitation to my playing is mostly on purpose. I want to know the fretboard well enough that I can accompany other people playing a song that I don't know and without recourse to tab or other music. I can do that on the guitar and mandolin and am working on being similarly proficient on the dulcimer. I would love to be playing a song when someone says "take a few verses, Dusty" and be able to improvise something melodic and fun for a while. But I can't quite do that now. Maybe at some point I will surely experiment more seriously with other tunings, but my goal right now is to know the fretboard in a 1-5-8 tuning. I am not "afraid" of other tunings in the sense that I will occasionally play around with one or take a workshop on DAc tunes or something like that, but I still consider my main "work" on the dulcimer to be getting better aquainted with the fretboard in a 1-5-8 tuning.