Also, as with a lot of places where algebra meets geometry, the 'homogenising' (in a good sense) effect of the algebra makes the geometry much less challenging than it could otherwise be. (Linear algebraic groups, which are a particular kind of scheme, underlie much of my research; but I understand way less about schemes in general than about the geometric structure of LAG's.) That's just to say that, from my point of view (as, admittedly, an algebraist), getting the solid linear-algebra background to handle Lie algebras as abstract structures is way more important to understanding Lie groups than a full picture of all the subtleties of differential geometry.

(With that said, anyone who wants to understand the geometry of differential equations will need at some point to handle a lot of non-homogeneous geometry, so my advice isn't the end of the story even for those who agree with it.)