I get the same thing from the same palm ( sabal minor ) any time I mist in the mini greenhouse really heavy..I will take the seedling out wipe the fuzzy mold off and it will stay away until I mist real heavy again..happened a few times over winter the plant seems fine and is pushing a new spear I wouldn't worry about it to much but others might have a differant idea.

There's a lot of different fungi that affect some plants but not others. So it's probably safer using the fungicide. One thing that aids fungus is lack of air movement. You could try using a fan. I remember years back going to the big pyramid glasshouse in the Sydney Botanic gadens. They were using large industrial fans to help reduce fungus problems.