Bradley Bergeron’s first professional job out of college was selling retirement savings investments to public schoolteachers in Connecticut. The applications he carried in his black leather briefcase, however, were for one type of product only: a high-priced variable annuity.

“From the teacher’s standpoint, they really miss out getting quality advice,” said Mr. Bergeron, 27, who sold the plans for Axa Advisors’ retirement benefits group. “People who are in the schools pitching them and positioning themselves as retirement specialists are really there just to sell them one product.”

Workers at private companies typically enroll in a 401(k) retirement plan approved by the employer, which is held responsible for the menu of investment options offered. But public school employees and people working for nonprofits and religious institutions are often exposed to brokers who operate in a more unruly marketplace under different rules, which are defined by a patchwork of state laws and less stringent securities regulations.

Brokers and insurance executives say it has become more difficult to walk into schools freely in recent years — the Los Angeles Unified School District, for instance, strictly forbids soliciting on campus.