BOSTON — The Dartmouth men’s basketball team is dropping its attempt to unionize, ending a push to become the first college athletes to bargain for a contract in order to avoid a potentially damaging precedent from a National Labor Relations Board that soon will be controlled by Republicans. Service Employees International Union Local 560 filed a request to withdraw the NLRB petition on Tuesday rather than take its chances with an unfriendly labor board. “While our strategy is shifting, we will continue to advocate for just compensation, adequate health coverage, and safe working conditions for varsity athletes at Dartmouth,” local president Chris Peck said in a statement that called collective bargaining “the only viable pathway to address issues” facing college athletics today. The Dartmouth players petitioned the labor board in 2023 for the right to unionize, saying the New Hampshire school exercised so much control over their schedules and working conditions that they met the legal definition of employees.