The point of 5e is to be flexible. If you want to play to your class's lore, you can do that! Druids very early get spells like speaking with animals and plants, for example. It's your choice to play that way or not.
But as for working stuff into the plot and story, that's up to the DM. You might just need to drop reminders ("I wonder if they know anything about my lost brother" or whatever). But if they really just want to run their story as written, you'll probably just need to find a different DM.