Ideally, I do want them to include some kind of leftover effects of your Shepard's "decision", such as green eyes for Synthesis, or reapers just... hanging around the Milky Way for those who chose Control. But then again, I get the sense that they don't want to have to explain to newcomers to the franchise "why everyone's eyes are green and why they're part machine and stuff", or what those giant synthetic squids are doing floating around in space... as well as what those giant squids are in the first place. They want to hook those little newcomers with new content, and Shepard's journey is very long. Explaining his "choice" would also mean explaining the entire trilogy, as well as explaining who Shepard even is... and at that point, you might as well just play the trilogy (though really, you should). My guess is that they're either going to come up with an explanation of why those choices aren't affecting the new game (a very meticulously-crafted reason, like "Lol the effects faded over time... or... something")-- or, of course, Andromeda happens before the end of the trilogy takes place...
Or it's a completely remastered version of Mass Effect where Shepard's journey never existed, and they make humorous winks and nods to the original trilogy to make sure devoted fans don't crap themselves with rage entirely (and I will say this now, if that is the case... that strategy will not work with me, as I'm sure it won't for many others. My pants will be filled with the crap of anger).
If the original trilogy does factor into it, and they're in their (Ark?) leaving for Andromeda when Shepard jumps into that green beam of death, then they won't be affected by the synthetic/organic amalgamation, because the Crucible probably has some kind of signal that only affects The Milky Way (because relays), and that'd be a convenient explanation that I'd have no way of confirming but would totally buy if they explained it hard enough... and when it comes to lore, everything is pretty much up in the air with the series (or any sci-fi series) in general. You could say "giant sharks are attacking" (or giant squids, lol) and make it sound 100% plausible with sci-fi if you put enough tech jargon in there. I totally believed the reapers could exist, because they explained it well. It didn't make sense, but I bought it anyway.
I also get the idea here that they want to forget that any of those conclusions even happened, and having a constant reminder of them is something they don't want. The endings were so notorious for being "the worst ever" that people who haven't even played Mass Effect know about them. Wasn't EA nominated as "worst company in America" after those endings happened? Yeah, people are kind of over it by now, but I'm willing to bet they still feel the sting. I'm sure they want to sweep Mass Effect 3's conclusion under the rug and say "no need to look under there." That's probably what I would do, too.
Personally, I'd no longer really look forward to Andromeda if it was a remaster. I might still buy it... but I'd be far less enthusiastic. They say that there is no canon ending, that Andromeda isn't a "Sequel", and that they believe in the player's ending choice. And if they don't want to include leftover remains of those endings at all to prevent confusion for the Mass Effect newbies... there's really only two explanations of what might happen.
And I hate that I convinced myself of that possibility.