Hey there! For most assets, Exodus is a "lite wallet" that doesn't need to download the full blockchain. However, XMR is an exception. It doesn't need to download the whole blockchain in order for you to send/receive XMR, it needs to download the blockchain to know what your balance is.

However, the whole blockchain only needs to be downloaded if your wallet has transactions dating back to the early days of XMR. Since this isn't necessary for most users, you can download a smaller part of the blockchain. We have a guide to doing so here.