The Sweden Democrats started as a anti-immigrant campaign and in the early years were mostly doing extremely blatant, racist, antisemitic and anti-black propaganda (stickers, posters, radio broadcasts) and organising demonstrations which attracted loads of neo-nazi skinheads. Leading to riots and attacks around their events. This was in the dark decade of the 90s, the atmosphere was similar in Sweden to most of Europe with neofascism returning to the open. Murders, arsons against refugee camps, the wave was everywhere. There are photos from their early years with officials wearing swastika armbands. Since in these groups we know historically that everyone wants to be the Führer they had the more radical individuals trying to coup the party leading to several splinter groups weakening them. This problem plus a very strong antifascist campaign against them led to them taking on a more “serious” path trying to get off the street hooliganism and into local politics/councils. They succeeded with that and have become more and more mainstream to be able to grow, so their party program is now very watered down from their original nazi roots. Their focus now is “law and order” and anti-islam and they attract the general racist, conservative, uneducated, by far mostly male and by far mostly rural voters. They get around 20 % of the votes for over ten years now, if I remember correctly.
Initially all other parties refused to work with them in any way but this has started to weaken in recent years and after the last election the new right-wing government (“tories”, cristian democrats, a mish-mash of right-wing conservatives) decided to take them on as a “support party” in the parliament. So they are not in the government but directly influence the governments actions with their support votes, without them the government would be too weak. It’s really awful.
But even if they are now the 2nd or 3rd largest party they still house open fascists. And there is scandal after scandal happening. Someone already mentioned the recent “sieg heil” thing in a comment. A few years ago there was a scandal where three of the party’s most prominent parliamentary individuals had a night out, getting drunk, harassing people on the streets which ended up with them gearing up with metal rods from a building site getting ready for “a fight”. Of course these stupid nazi fucks filmed it all and it was leaked to media. So the party is forced to do cleanouts of these problematic individuals very often, but the party somehow STILL maintains more or less unaffected in the polls. Even though this self-proclaimed “law and order” party obviously has bonehead thugs in their leadership. It’s laughable. But tragic. It says a lot about the voting grounds in Sweden, there is so much everyday-racism.
With that said, Sweden is not really more racist than most other countries in Europe, I would even argue less so than most. This problem is identical everywhere, racism/fascism is deeply rooted culturally.
I hope this helps to understand this shameful party.