I don't know if there was really a stigma, so much as the culture of the 00's was dominated by the fallout of 9/11, which brought certain realities about the world to light.
The mood of the whole west changed on that one day, and it introduced all kinds of anxieties that we're still grappling with, that went alongside the lies about WMD's, widespread loss of faith in our political and economic institutions, as well as a paranoia about each other. The awareness of climate change grew. The future seemed less and less likely.
You saw the sudden re-emergence of mindless inhuman destructive forces like zombies or godzilla type monsters or vampires. Post apocalyptic scenarios were the order of the day.
At the same time you had an explosion in YA fiction brought on by Harry Potter, and publishers scrambled to capitalise on the sudden profitability of this sector. YA bought the hunger games, maze runner and so on.
Widespread pirating, the internet and meant that film-makers would only invest in tent-pole movies - spectacles only really suited for the big screen - these were most suited to movies about superhuman characters with exaggerated characteristics facing threats that caused massive damage - transformers, avengers relived the destruction of 9/11 over and over.
The wars in Iraq and Afghanistan, and the moral unease with them brought movies like The Hurt Locker, Black Hawk down and series like 24 and homeland.
In light of the realism of post-apocalyptic concerns, sci-fi which is essentially positive in outlook (humanity lives long enough to become space faring) seemed a little old hat. The gloomy or the cynical or the escapist were the order of the day.
The star wars prequel trilogies failed to make the expected cultural impact.
In addition there were pragmatic realities of sci-fi movies in particular - there were perceptions about their audiences that couldn't justify the kinds of budget that would be needed for special effects: too few, and too nerdy for mainstream appeal. As we've seen with the rise of sci-fi since Avatar, this turned out to be false.
So I don't think the early 2010's was when sci-fi production was at its least as that's when it started to turn around - the re-emergence of star wars etc. would have all been planned as a result of Avatar's success, as studios realised they could exploit this market.