Vitamin pills are usually taken orally or sublingually. If I crush them inside a blender as a part of a shake, would it compromise their function?
Only a study in which someone would put different vitamins in a blender and measure the eventual changes in their activities could answer this question. Everything else is just a guess or estimation.
Next, the question would need to be for a specific vitamin in a specific chemical form and in a specific tablet.
My estimation is that nothing significant would happen. Some vitamins could be partly destroyed by heat, but blending alone does not produce much heat, anyway. Crushing of the tablet could affect the physical composition of the tablet and result in either slightly decreased or increased absorption of the vitamin.
On NutritionData, there is a chart with estimated effects of drying, cooking and freezing on the vitamin content of foods. For example, cooking (it does not say for how long) can destroy 25% of vitamin A, 50% of vitamin C and 70% of folic acid.
I think, in general, blending would not do nearly as much damage as cooking.