Does anyone know how to convert NetCDF files generated from a climate model into any GIS-compatible format? (GeoTIFF, ESRI Shapefile, ASCII, CSV, etc.)

NetCDF is a very open format, meaning that the contents can vary a lot and it's hard to give a very specific solution without knowing the requirements. For example, a single NetCDF can contain several rasters with several bands each, where the bands may or may not contain color information.

In my experience, the RasterBandSeparator is very often helpful when working with NetCDF conversions, in particular look at the output attributes _raster_index and _band_index to keep track of each individual "dataset" inside the NetCDF.

For the attributes, they are mostly represented as lists in FME, so you should look at the ListExploder and ListIndexer.