The short answer is that you can't.
You don't want to disable Google's authentication safeguards - and, generally speaking, you can't (because they not only protect you; they also protect Google - as well as the Internet ecosystem as a whole).
Even if the user doesn't care about a specific account, Google itself might still care - for very good and practical reasons. For example, when a spammer compromises a "throwaway" account to send spam ... a bunch of people would be spammed, which would be reported to Google as spam ... and Google would then have to investigate and clean up the mess. (And this is only one example of how giving users an option to disable these measures would have its own operational burden; there are many more.)
So I'd like to answer your more broad, implied question - how to efficiently use GMail and its security features while traveling and regularly changing devices:
- Install Google Authenticator on an extra/fallback device that you will always have with you, even without service. It provides the second factor - even when you are offline and cannot receive texts. Once installed, the phone that holds Google Authenticator requires no service at all (but you still have to have the device with you).
- Use a U2F key. This provides the second without having to have a complex device at all - just a sub-US$20, no-power-required USB device that fits on your keychain. This requires that you're reading your GMail on a system that has a USB port. (There are also fobs that speak NFC).
- Print the ten backup codes provided by Google, and use them when you don't have the device that carries Google Authenticator. This is sub-optimal because you can only use them once per device/session (so it's probably not really an option, but I'm including it here for completeness)
You might also experiment with creating an app-specific password, but I don't expect this to work well for your use case (because Google's "you are coming from somewhere weird" heuristics would probably activate).
One of the first two options should fit most use cases. To maximize your chances of being able to log in, I'd actually recommend both GA and U2F.