Colorfast(ness)

Colorfastness refers to the tendency of fabric, usually in clothing items, to hold its color. Tests for colorfastness include subjecting the fabric to light, washing with cleaning products, and rubbing. If a fabric is not deemed colorfast, or if the information is not available, it is recommended that it be washed/dry cleaned with like colors or alone until color loss is reduced. There are some products on the market, one is called “Retayne” that aids in binding dye particles in the fabric to minimize color loss. (See also, bleeding and crocking)
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The old rule from my 7th grade Home Ec teacher still stands. Treat the fabric BEFORE making a garment/project exactly the way you will AFTER it is completed. If it will be laundered, wash it before. If it will be dry cleaned, ditto. Avoid unpleasant surprises and possibly ruining something you have worked hard on.
Do I wash fabrics I plan to use in my vestments? Generally not, with the exception of batiks. They hold a lot of dye and sometimes this can migrate to fabrics they touch in the hot, humid summers in CT.  I construct my own orphrey bands and this is where the problem might arise because I like to use batiks.   I use natural fibers and fiber blends for the main body of my chasubles and I usually dry clean these before construction begins.  
Don't forget to test trims for colorfastness as well.   Sometimes these can shed dye.   Always test BEFORE to avoid problems afterwards.