What Are Your Rights If Border Agents Want to Search Your Phone?

The US civil discourse sometimes strikes me..

For example if the biggest (?) US newspaper advises you to travel with as little data as possible because the gov. border controls are percieved as morally outrageous and there's just no practical way to deal with this issue other than hiding.

I know TSA looks for communications with extremists over Facebook or something. But why would they think they could identify suspicious activity in such a short time? They aren't professional or competent enough to join real law enforcement, why do they pretend to be intelligence officers?

If someone wants to join a terrorist organization or something, and the FBI didn't identify them by the time they get to the airport, TSA ain't stopping them. So just let us pass in peace

I've been traveling internationally for years, and am scheduled to go in a few months to the Dominican Republic. The only part of the trip that is giving me anxiety is returning to customs. I'm not sure what my best course of action is at this point. Go and hope for the best? Leave my phone at home and deal with the inconvenience?