It's always a question of where the seams show, isn't it? The most obvious connection is through ancient precursor races, where Prothean ruins get compared to Rakatan Infinite Empire tech. I've read a few where a Mass Relay is found in the Unknown Regions, and that works cleanly enough. The bigger stretch is making the Force and biotics feel like they're part of the same underlying reality, and honestly, most writers don't even try—they just let both magic systems exist side-by-side, which can feel a bit messy. Characters tend to mesh better than the lore. Shepard and a Jedi Knight arguing philosophy while geth and battledroids duke it out in the background is the real draw, not the technobabble explanation for the crossover.
Honestly, my favorite takes are the smaller-scale ones that don't try to merge galactic histories. A story where, say, Garrus gets stranded on Tatooine and has to fix his omni-tool with scavenged Jawa parts feels more genuine than another 'Reapers vs. the Empire' epic. Those huge wars can get repetitive. The blending works best in the character moments, the culture shock, the little details like a turian trying to understand why humans would build a weapon the size of a moon when a Citadel dreadnought would do.