How can I remove the material where these two object meet? I'd like to keep the objects separate, but I imagine a vertical line right down the middle of these two objects.
Create an Empty (plane axes). This will be the mirror line.
Delete one of those "bars".
Select the other one and add a mirror modifier, and set the mirror object to the Empty.
Position the empty so that the bars are where you want them to be.
Go into edit mode and reshape the end of the bar by selecting verts and moving them. Get it to the look you want.
To turn both back into separate objects again apply the mirror modifier, go back into edit mode. Select everything with A, and press P and choose "Seperate By Loose Parts".