This is a typical talking-point of Sverigedemokraterna - the claiming that discussions around immigration are taboo in Swedish media. The major issue with this is that it's not actually the lack discussions about immigration (immigration-related actions and decisions by the government and the municipalities are frequently debated in "mainstream media" and commented on by editorials) - it's simply the fact that the majority of the Swedish people don't agree with the policies suggested by Sverigedemokraterna. If you listen to someones arguments and rejects them, are you then avoiding the debate just because you have rejected the arguments?

I will say that the Swedish population has become more polarised over this question - both the number of people who claim "immigration is good for Sweden" and "immigration is bad for Sweden" has risen over the past 10 years, shrinking the middle. There is also a strong correlation between education and attitude to immigration (in 2011, 56% of the people who had only 9 years of education agreed that reducing the number of asylum seekers to Sweden is good while only 22% of those with a university-degree agreed with the statement). This might explain some of the frustrations showcased by the people supporting Sverigedemokraterna and other anti-immigration parties - they might simply lack the ability to debate in the way public debates are typically held and coherently express their ideas in a convincing way.

Even if the case is that immigration is public debate in Sweden (and I don't doubt that), Sverigedemokraterna's success (in addition to the underdog status given by the media) is in part due to a feeling of taboo for their point of view. A frustration boiling to blow the lid.

The lack of immigration debate in the 1990s is what caused Dansk Folkeparti to gain enough support, that from 2001 to 2011, they could control the Danish government. So even if Sweden's immigration debate is happening, immigration debates always happen too late.

(But this is not unique to immigration.)

That's not true. There is a vivid debate around immigration and asylum issues in both old fashioned- and social media.

Sverigedemokraterna is big because a large slew of the Swedish population is slanting toward racism and are prone to accept simple "solutions".

You oversimplify things. While you are to some extent correct I do not think that was the main reason for their surge in the last election. One contributing factor was the bullying from media and the other parties before the election where they were not allowed to participate in debates, all parties declared they would never cooperate with SD, and several newspapers ran anti-SD articles the day of the election. This strategy backfired heavily since everybody loves an underdog, and the faulty idea that if everyone wants someone silenced they must have something important to say.

There are also other factors like that some people genuinely seem to believe that SD has cleaned up their act.

EDIT: I am personally strongly pro-immigration (much more so than any party in Sweden) and I have to disagree about there being much debate about immigration in traditional media. There is a lot in social media though, so I have no idea where all the racists get their idea that they cannot debate immigration issues anywhere.