I am considering trashing my old sneakers and only bringing my flip flops on my next trip, but I'm going to be stopping in several different countries so I thought it was worth researching this.
Can you wear open toe flip flops or sandals on all airlines / airports security or do any countries or airlines prohibit this for security or cultural reasons?
I usually wear really open sandals and have never been told not to on a plane. But I have been told proper shoes are needed when walking through trains in Canada.
Caveat, I have not travelled all over the world and not used all airlines so there might be some that do have restrictions.
Besides safety in traveling there is passing borders. I have always decided to look well dressed for border crossings, even as an adult European woman. If your entry into the countries of your choice is less a given you need to be even more careful. Nice, new looking, sandals fitting with outdoorsy clothing that looks pretty new and clean will raise no problems. But old or cheap looking clothes and footwear may lead to extra scrutiny, extra checks whether you have enough money for your travels, extra looking in your passport to see if all visa are right and so on.
I would advice you to wear 'normal' shoes which fits with your clothes and all of that clean and whole. Crocks are really on the cheap end of acceptable if you are from a country which people are able to travel easily over country borders.
Women can get away with sandals more easily but if you go for open footwear it better looks like fashion rather than cheap.