Now you said "machine applique". Are we jumping to conclusions that it's on an embroidery machine? Or is it on the sewing machine? Either way, blanket stitch involves more changes in direction and the one tiny stitch at the base of the loop, so it's much harder to get the stabilizer out.
I don't hesitate to wash embroidered items that I plan to give as gifts because washing before I do the work helps to prevent puckering that might happen if there is shrinkage after the item is embroidered and washed. Also, recently I tried using some tea towels from a common, popular source and found that they wrinkled like crazy in the dryer. Who wants to iron tea towels? Ugh. Worse yet, they will need a hotter iron than my embroidery thread can tolerate. Better to find out ahead of time.
Not all wash away stabilizers are the same. H2O Eau Gone is a particularly sturdy one for underneath that I like to use with just about everything I do on the embroidery machine except quilting. I try to use less expensive types of cut or tear away stabilizer but always go back to that if it's an item that will be washed. If the fabric is stretchy or doesn't have much body I use a very slight mist of temporary adhesive with the Eau Gone. Pellon Wash n Gone is also acceptable and easier to find locally. Sometimes I have to use two layers of it, and that's no saving. Vilene is another brand that is very good. I have not used any of this stuff for sewing machine decorative work, but see no reason why it wouldn't be just as effective that way. I would use spray baste with it.