See, the problem I have with this sort of thing is the usage of the terms 'Islamic' or 'Muslim' society and the like. To me (as a Muslim) that label doesn't really make much sense, in that you have various 'Islamic' societies (really, just societies where the majority of the populace is Muslim) that differ very radically in terms of basic politics and the like. It is definitely true that in traditional (particularly Arab) society, homophobia is a huge, huge problem but this sort of march doesn't have anything to do with that inherently - it is more about striking out at a minority community. I'm not sure what the broader Muslim community in Sweden is like, but I know that 40% of American Muslims support marriage equality and LGBT rights in general - not a majority by any means but very close. European Muslims tend to skew slightly more conservative (not inherently because of any flaw there but all sorts of xenophobic reasons that push them into being incredibly insular, tight-knit communities) so it may very well be that the community in Stockholm has conservative elements...

But then the question is would this right-wing group be hosting a LGBT Pride March through a Swedish conservative neighborhood and city, just to rile them up? I highly doubt it. Either way, a very, very contentious issue.