Combine butter or margarine, shortening, and sugar in a mixer until creamy. In a small bowl, whisk together the egg replacer and warm water until foamy. Add egg replacer mixture, vanilla, and "safe" milk to margarine, shortening, and sugar mixture. Mix until smooth. In a separate bowl, combine flour, xanthan gum (if using-see notes), baking powder, and salt. Gradually add the flour mixture to the margarine mixture until combined. Cover dough and refrigerate for 1 hour.
Remove dough from the refrigerator and divide in half. Put half of the dough back in the refrigerator. Place the other half of the dough on a floured surface (rice flour works well). Roll it out to about ¼ inch thickness. Cut out shapes using cookie cutters. Transfer to cookie sheets. Repeat with remaining dough.
Bake at 375° for 6-8 minutes. Edges should be firm but not browned. Remove from cookie sheet and transfer to cooling racks. Top with "safe" frosting.
Notes
*Omit the xanthan gum if the gluten free all purpose flour blend you are using already contains it.