Emma Torres, an immigrant from Ecuador, said a human resources employee at the club in Bedminster, N.J., crossed her name off a list after she said she did not have legal status.
Trump officials hope to a close deal on their plan to make asylum seekers wait in Mexico.
For asylum seekers who spent months walking to Tijuana, the decision is a dramatic reversal.
Hundreds of Mexican federal police officers took up positions at a sports complex where 5,600 migrants are camped.
Authorities say that about 100,000 people legally pass through the San Ysidro border crossing every day.
Trump administration has won support of leftist president-elect Andrés Manuel López Obrador, who takes office Dec. 1.
Smugglers cut deals for migrants traveling with kids. The U.S. sees a humanitarian crisis.
A Mexican official said that current Mexican immigration law does not allow those seeking asylum in another country to stay in Mexico.
The protesters said they fear that the caravan will increase crime and hurt the community. Others volunteer to help the migrants.
The search for Mexico’s disappeared — people who have been killed but not found — is one of the saddest rituals of the country’s decade-long drug war.