This is bound to happen sooner or later. We each have individual tastes, and it's a good idea to make easy and nutritious alternatives available to everyone in the family in case they don't like what is being served. There's no need for you to COOK more than one dish -- kids can prepare a simple Plan B themselves.
It's fair for parents to request a "good sport bite" -- just one teensy bite to see how it tastes, so kids don't miss out on something yummy just because it looks funny. If they don't like the taste, then a good ol' pbj sandwich will suffice for backup. Don't make a big deal about it. Eating is not an area where you want to engage in power struggles!
Simply excuse your child from the table so he can make a sandwich and bring it right back to eat with the family. Even at age three kids can assemble a pbj sandwich with a plastic knife while you stay at the table and enjoy your meal.
You may want to discuss this ahead of time, and teach your child the language you'd like to hear. Mommy, I took a good sport bite of the okra, and I don't like how it tastes. May I please make myself a sandwich instead?
You'll also want to teach your children how to handle this situation appropriately for times when they are a guest in someone else's home. Remember to tell them to take very small portions of any questionable foods that they want to try -- they can take a second helping later if they like it.
Teach them how to compliment the chef on the foods they do like, and how to graciously deflect questions about the ones they don't. Kids don't just naturally know the language for these situations, and they need your guidance and example to learn good manners. And "good manners" rarely, if ever, require us to eat something that we find revolting!