Passing through security at the airport during domestic travel requires acceptable identification documents. The Department of Homeland Security (DHS) has designated several acceptable forms of identification including passports, a border ID card, or, a trusted traveler card such as Global Entry.
In 2020, only REAL ID-compliant cards will be accepted for air travel and if a traveler is out of status or is in unlawful presence, the traveler should obtain alternative acceptable identification documents, which includes a valid passport issued by the government of which he/she is a citizen.
Generally, traveling with a passport with no valid U.S. visa stamp on it does not imply unlawful status. The DHS explicitly cautioned federal agents from assuming that non-possession of REAL ID-compliant identification cards indicate that the traveler is an undocumented immigrant. However, given the current political climate, the restrictive immigration policies and the heightened immigration enforcement rules, it may be a trigger for further inquiry if the TSA or any federal agent exercises discretion of the need to determine lawful presence.
In the meantime, considering the implementation of the law is not until 2020, there is no need to change travel domestically.
Instead, it is advisable to use this time to determine whether there are legal options that one may now undertake to obtain lawful status before the full implementation of the REAL ID Act.