I have a mission for both Minutemen and Railroad to settle Sunshine Tidings. I have already completed the Railroad side of things and turned in the quest, but the mission to build a radio for the Minutemen is still available. Does that mean I can do both?

Yep. You can do both. The Railroad just want it as a safehouse.

If there were two factions in the game that would get along, it would be the Minutemen and the Railroad.

Cheers mate, Id better get building that radio. I had a feeling they'd be better bedfellows.

Siding with multiple factions is one very nifty aspect of Fallout 4. Not sure if it was quite like this in other Fallout's because I always just sided with one and went with it.

I'm siding with everyone in FO4 except The Minutemen right now.

I watched the BoS, Institute, and RR get in to an epic battle at Bunker Hill. I just hid out of the way and collected the loot from the casualties afterwards. I was killing synth's just to see what would happen and if they would turn on me but they didn't. I'm still doing quests for all of them.

You also get asked by settlers to settle other places as well without the request coming from a designated quest giver. I send all my companions to Red Rocket. I couldn't assign a companion to gather food or be guards so I put up a beacon to attract a few settlers and assigned them. After a while the settlers would randomly start giving me quests to go on for other places to clear out that would make good settlements.