You asked

What should I do if the local culture discourages breastfeeding?

When you are travelling to other countries or to a place where there is a different culture, you have to make sure that you can respect it as sometimes you mind find yourself in trouble if you do not. That may not be good for your baby, especially if you are travelling with him.
Before deciding which country to go to, make sure that you have done your homework and you have already done your research about the cultures and beliefs of the countries you have in mind when it comes to breastfeeding. In some countries, breastfeeding even in public is fine while in others it is highly inappropriate. If breastfeeding is not allowed in public, then you just have to make some adjustments to avoid getting into trouble. Breastfeeding your baby in private should not be hard for you, especially if you have prepared for such situation.
So when you are travelling, do not forget to bring your breast pump with you, so that you can do something if breastfeeding in public is prohibited in the country you are visiting. Since you are in a different country, it can be hard to predict when your baby will be hungry, so having a breast pump will allow you to stock your milk in a clean feeding bottle. You can then take this when you are out and you will therefore not have to rely on breastfeeding your baby while you are outside. 

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