What counters astringency?
Many leafy and dark green vegetables have high tannic and dicarboxylic (including oxalic) acid levels. Though these are weak acids, they have a powerful astringent effect. Some of the main tricks to hiding and/or removing these are soaking in:


Ascorbic acid (vitamin C, lemon juice)
Fats
Food grade lime
Milk


So if your smoothy is milk based you will be extracting the maximum tannin from the spinach :-)

A pre-soak in a small quantity of milk and then discarding that milk, or a pre-soak in lemon juice and then a quick fresh water rinse are probably the simplest "fixes" of the spinach's astringent effect