This is not an issue to me. I hate amiibo, they're probably the worst example of DLC I can think of. I hated Awakening's DLC, too. It was overpriced and not remotely compelling.
How I deal with these instances of DLC is by not buying them. I miss out on a small amount of content.
This is so much different. This is not the half-assed Awakening DLC, nor is it the bite-sized bits of content rationed off for use as amiibo support. This is two separate games with different gameplay content and different storylines featuring the same characters. Someone mentioned the Zelda Oracle games, and I think that's an apt comparison. I might even compare it to Ocarina of Time and Majora's Mask, if the two had released simultaneously.
The difference between those two examples and this new Fire Emblem is that Fire Emblem gives you the option to buy the second game -- an entire new game's worth of content -- for something like 40% its base price as DLC. We still know very little about the games, obviously they have to be worth their $40 value, preferably by having the same amount of content as Awakening sans DLC. But if they're that big, and distinct from each other, I would have no problem paying $15 for an entire additional game with an actual story, as opposed to the $50 worth of garbage DLC they sold for Awakening.
For those complaining about having to buy a new SD card, I highly doubt the second game as DLC will take up as much space as a full game. It will use the physical game you bought for character models, music, etc. There may be some different characters and music, but I'm sure the DLC will be smaller than downloading the whole game separately.