When the taste is truly to be avoided, take a sip of a drink before un-pinching your nose to avoid any taste left on the tongue. Slosh the liquid around your mouth for good measure. If you’re eating in public or anywhere where you can’t politely pinch your nose, exhale immediately before taking a bit/drink to avoid the taste. Be sure to take a small bite if doing this to avoid choking when trying to breathe again.
Cotton swabs such as Q-Tips are a discreet alternative to a paper towel, though you’ll most likely need more than one. If you know just when you’ll need to eat something unpleasant, try to refrain from having any water beforehand during the day. Drink caffeinated drinks like soda or coffee to dehydrate yourself; your mouth should be reasonably dry come time to eat.
For a more uncomfortable alternative (though preferable perhaps if you have teeth which are sensitive to cold), you can scald your tongue with a hot drink like tea, coffee, or hot chocolate. The heat will make your taste buds much less sensitive in the moments after sipping something really hot.
If you’re underage or have no access to hard alcohol, try a hygienic mouthwash which contains disinfecting alcohol such as Listerine. This too will help to numb your taste as well as distract with (usually) a strong mint flavor.
In theory, you can do this with any spice (sugar included), though salt is usually always at hand and salting to excess rarely draws any attention.
Spearmint extract will have the same menthol quality as peppermint and is an adequate replacement. If you have no extracts of the mint variety, you can also reach for over-powering tastes such as almond or chocolate extract. Coat your mouth in the same way (using only a capful) and whatever you eat next will take on the flavor of the extract.
This is same logic can be used with food. Push whatever you’re eating to the sides of your mouth and chew alongside your cheek so that the food cannot reach your tongue. Try and keep your head tilted back slightly to encourage your food/drink to leave your tongue quickly and continue down your throat.
Many toothbrushes today include their own tongue scrapers on the reverse side of the brush head. Look for these for an economic option.
If there’s a particular cuisine you avoid, consider it again at a restaurant you’ve never patronized. One which is well-recommended online or by friends. Never let one bad experience turn you away from something entirely. If there’s a particular dish which you’ve found middling or inconsistent, try looking up recipes online and learning to cook it yourself. When you cook for yourself you’ll have ample opportunity to alter the dish to your taste.