The other Earths are completely irrelevant in terms of tidal forces in that situation, so they won't cause any issues in terms of tidal locking. The more massive moons would likely cause the Earths to be tidally locked to their own moons, though. (There still would be a day night cycle there, though, it would just be close to a month long)This picture is taken from one of Sean Raymond's Planet Planet articles, Cohorts of co-orbital planets.
What the article doesn't explain, however, is the basis for the question. In a solar system in which six rocky planets, each one the size of Earth and each one orbited by a single moon 1/4 its mass from a distance of 238,900 miles, orbit their sun from one same distance, would a 60-degree difference allow each of the "Earths" to spin in day-night cycles?
The larger moons cause roughly 20.3 times as much tidal force as our moon does (Due to the larger mass and same distance)
The closest other Earths cause 0.0000017 times as much tidal forces as our moon does.