Mass Effect is a money making machine. BioWare and EA would probably have to be crazy to not want to continue the franchise in whatever way they could. As to how they will continue it, your guess is as good as mine.
Drat, I keep forgetting the Refusal Ending. Just a completely foreign concept to me, I guess. I still think Synthesis can work with the rest. Those changes would be drastic initially but given a generation or two, could subside into background 'color' like all the other endings (except Refuse). No canon ending need be endorsed and the MW galaxy spins on. Still, the continuation of Andromeda is the more likely scenario.
As for Shepard's preferred gender option - the only place I recall that being an issue (and it's been some time since I played MEA) was during Alec's memory speaking with Garrus's father about Commander Shepard's Reaper reports. I seem to recall them having to use a pronoun in a couple of spots. I can't recall if it was necessary for any codex entries or mentioned in Liara's messages. That's the only impact 'the most famous human in the galaxy' had on the next galaxy/chapter - a vague footnote.
The gaming industry seems to have currently pivoted their concerns from gambling on the next game pleasing consumers to focusing on methods making enough money to please investors. It's not about players. It's about payers. It's not games - it's revenue streams. Similar to the comic book market some years ago, investors realized how much untapped revenue potential was contained in the gaming geek market, and decided to dig into it. That's why so many games are now marketed with an eye more towards investors than to players, with microtransactions, loot boxes, and other monetisation scheme-ware. I don't think these business models are going anywhere anytime soon, but I also think nature abhors a vacuum and when somebody presents good games, well-made, and complete, their profits will soar on the goodwill of a gratefully respected audience.
I am not sure ME will have a future. The MW story is finished and there is little of value that can be added to it. I really liked andromeda and even though it was not a commercial failure it was incredibly poorly received. Furthermore the feedback of why people didn't like it is conflicting and often has very little grounding when compared to the original trilogy (no Shepard= not ME, bad writing/ story, boring races while in the trilogy we can describe entire races with 2 sentences, characters aren't fleshed out while MEA has the most extensive crew quests of all the games). Basically from a devs point of view ME is a franchise that people suddenly don't like for no reason. It hurts me to say it but I doubt EA will take the risk of making more ME titles. (Hope they will however)
It's okay, Marolf. Given that blatant opening left at the end of Andromeda, there was every reason to believe a follow-up, Quarian/Miscellaneous ark DLC was in the works. It was a rude disappointment to everyone when that cancellation-in-favor-of-book was announced.
That N7 video was very nice and a whole lot of nothing. Everybody knows everything at Bioware is essentially bottlenecked by Anthem right now. It's not a game for me but I hope it does well enough to establish a decent revenue stream for Bioware so they can continue to develop their classic RPG's with less of EA steaming up their tails. Time will tell.