My take is that the stain, while for exterior use is not a finish. Stains are typically made up of dyes, pigments (ground up colorants), solvents, and a weak binder. The BriWax also has a solvent that evaporates before you buff it. I'm thinking the wax slightly dissolved, or softened, the stain, the two intermixed and caused the blotching you have. I would have top coated the stain with a varnish prior to applying the wax. Mineral spirits should remove the wax (and the stain), and you'll have to start over. There may be alternative solutions, but that's my take.
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