In January, at an annual lobbying day in the State Capitol for Muslims, Molly White, a state representative, told her staff members that any Muslim who entered her office must be asked to pledge allegiance to America and its laws and to renounce Islamic terrorist groups.

The Texas Legislature is also considering a bill, similar to ones passed in other states, that would prohibit basing decisions in state courts on foreign legal codes. It was proposed by conservative activists who contend that the goal of Muslims in the United States is to gradually impose Islamic law, or Shariah — an assertion that Muslims say is false.

Supporters of the Texas bill say that it is not anti-Muslim because it would prohibit the use of all foreign laws, not just Shariah. But for many Muslims here, the bill and other recent episodes amount to painful local evolution, with the old power structure of Texas struggling to make sense of a complicated, more diverse present.

Many Muslims here defy easy categorization. They embrace their many identities — as Texans, Muslims and Americans. Many of them are registered Republicans. One former community leader, a Syrian-American businessman with ties to Garland, served in 2013 as prime minister of a Syrian opposition coalition’s interim government.

For some, the shooting in Garland led to fear; the day after it happened, a 59-year-old man at a mosque in the neighboring city of Richardson was punched and kicked by two men as he left a prayer service. Although the man told investigators that he believed he was most likely not targeted for his religion or ethnicity, the attack remains under investigation and has added to tensions.