Hello Peter! I am a US Permanent Resident since 1997. Should I be concerned about traveling internationally at the moment, US politics being what they are? Or is it safe to assume that if I leave the country for a short while, I'm not going to get turned away at the border?
Even in this environment, I wouldn't worry at all about traveling as long as your primary residence is the US and your trips are each less than 6 months in duration.
Obviously not the OP. Another common reason is that a good number of countries do not allow dual citizenship. So you'd have to give up your "original" citizenship...