A presidential visit here that is intended to emphasize the growing influence of Mexican-Americans may serve instead to advertise President Carter's political liabilities in the Mexican-American community.

Carter plans to spend Friday night with a Mexican-American family in East Los Angeles, home to more persons of Mexican descent than any place except Mexico City. When he gets up to read the morning newspaper, he will find a full-page ad declaring, "We have doubts about you, President Carter."

The ad, sponsored by a wide range of Mexican-American organizations, complains that Carter has refused to deal with the troublesome problem of Mexican immigration and that he has failed to appoint Hispanics to policy-making positions. It also objects ot administration employment policies and to Carter's conduct of U.S.-Mexican relations.

We are Mexican-Americans to whom you have made many promises when you were campaigning for the presidency in 1976," says the ad. "In our view you have kept none of these promises."

Mexican-Americans are an increasingly crucial segment of the electorate throughout the Southwest, where they frequently hold the balance of power at the polis. Carter's margin of victory in Mexican-American precincts fell below traditional Democratic margins in 1976, which is one of the main reasons he lost California to Gerald Ford.

This time, Mexican-American voters are a key source of strength for Carter's most likely 1980 Democratic presidential rival, California Gov. Edmund G. (Jerry) Brown Jr., who has made highly visible government appointments of Mexican-Americans. The general view among politicians in this state is that Brown is far more popular than Carter with Mexican-American voters, although both would most likely be eclipsed by Sen. Edward M. Kennedy (D-Mass.), if he were to run.

But the protests that Carter will face this weekend are more reflective of genuine policy differences than of political personality preferences. When Carter meets Saturday morning with the state's six Mexican-American legislators, all of them Democrats, he will hear substantially the message that will be conveyed by the protest ad.

Specifically, says Assemblyman Art Torres of Los Angeles, the legislators want to discuss immigration, employment and the appointment of a Mexican-American to replace Ambassador Patrick Lucey in Mexico City.

"Carter's been quick to learn the Spanish language, which is admirable," says Torres, "but there hasn't been an ability to transfer his learning to important issues."

What Mexican-Americans want most of all is a policy that would allow illegal immigrants already in this country to become full citizens. Carter proposed a limited-amnesty citizenship plan that has languished in Congress without much apparent push from the administration.

Carter's trip to California this time will be a striking departure from past appearances in which he addressed a fund-raiser in Los Angles and then left town. After speaking Friday in San Francisco at a benefit for the family of slain San Francisco Mayor George Moscone, Carter will spend the night at the home of Stephen and Gloria Rodriguez in East Los Angeles.

Rodriguez, a former aide to Los Angeles Mayor Tom Bradley, works in the city community development agency.His wife is studying for her master's degree.

After his meeting with the legislators on Saturday morning, Carter is scheduled to address a Cinco deMayo celebration, a traditional festivity that commemorates a historic victory by Mexican troops over a French expeditionary force on May 5, 1862.

Cinco de Mayo celebrations have long been a favored haven for Anglo politicians who are trying to make points with Mexican-American voters. In recent years prideful Mexican-Americans have become increasingly skeptical about this approach. And they are particularly skeptical about Carter in the wake of his troubled visit to Mexico and his well-publicized wisecrack that he suffered "Montezuma's revenge" on a previous trip there.

"This administration has been completely insensitive to Mexican-Americans," says Manuel Lopez, organizer of the protest ad. "Now the president wants to eat a few tacos, listen to the mariachis, pat some Mexicans on the back and see them again at election time. It's a very cosmetic approach."