No, these drugs do not affect digestion in any clinically sigificant way assuming therapeutic serum concentrations. Blood thinners do not "thin" the blood in the way that one would think of it (e.g. they do not cause hemodilution and are not colloid/crystaloid volume expanders like NS, Hartmans solution, or Ringger's lactate, certain lipid emulsions, etc.), but rather posess antiplatelet properties- e.g. they prevent platelets from sticking together usually by inhibiting a clotting factor. The ditary restriction flow from the fact that certain vitamins are chemical precursors to clotting factors- particularly vitamin A and Vitamin K. In fact these vitamins are used to reverse the effects of some blood thinners, such as sodium warfin in cases of poisoning.

Betablockers act on CNS beta receptors and supress the effects of adreniline/epinephrine causing vassodialation and decreased heart rate. However, they have no effect on the production of HCl in the stomach. Most substances cannot be absorbed through the stomach, Ethanol is the rare exception, such that these drugs have no effect on digestion at the level of the stomach.

However, some beta blockers (metoprolol and propranolol were studied) do speed up GI motility (increased parastalsis) in dose-dependent fashion at the level of the esophogus sigmoid colon, but the effects were marginal at therapeutic serum concentrations, and other beta blockers were shown to have opposite effect.