Regarding refraining from observing prayer in some local mosques due to different praying time they maintain, Sheikh Muhammad Nur Abdullah, states that calendars are based on astronomical calculations which may slightly vary and the differences in praying time in local mosques are usually not that great. Hence, that variation should not make one go against the unity of the community.
So, if you are praying with the congregation in the mosque, you have no other option but to follow their timing. But if you are praying home, you have the option.