Backpacking through Indonesia during Ramadan (Bali and Gili) [duplicate]

My girlfriend and I are planning to visit Indonesia this summer from 3-24 June. When we were planning the trip we found out ramadan is from 15 May to 14 June.

We were first planning to start our adventure in Yogyakarta and make our way east slowly. We were told Java is mostly islamic, which would force us to plan our journey as we need to buy public transportation tickets beforehand. So we adjusted our plans and want to go to the less-islamic Bali, Gili islands and Lombok.

This leaves us with a couple of questions as we don't want to disrespect any locals:

• Is Bali/Gili/Lombok the best choice for us to travel to instead of the more islamic Java?
• How is public transportation on these islands during Ramadan and the holiday-week after?
• Do we need to book our accomodations/transportation in advance for these islands?

I found some answers on this forum, but this was mostly for the Gili islands, which doesn't seem to be affected by Ramadan.