doma, while not explaining everything, in general a few things are in play;
increased reporting: it is pretty recent that this area is referred to as autism spectrum disorders, and by bringing in he high functioning population perceptions of stigma have relaxed, more and more are diagnosed and reported.
aging parents: the New variation I referred to earlier, spontaneous changes at the sperm/egg level that can be comparatively massive occur at significantly higher levels as we age.
In other words, if we do genetics on 20 year old persons sperm and one who is 40, we see that the fidelity of genetic representation falls pretty dramatically, that is old people make knackered sperms and eggs.
There has been a massive shift in the age of the procreators.
this is definitely a component of the rise.
so:
reporting
aging mama's and papa's
more?
yes, it looks like there must be more, the best guess can't accommodate the change using the above 2.
The vaccines? Seems the swede's have looked pretty carefully, it doesn't seem to hold water, I am not familiar with the primate stuff you refer to. The actual coincidence of things like brad MMR and autism is actually pretty poor if one looks more closely.
If one is to make a cause and effect statement, the cause must really predate the effect, and the relationship should be pretty tight if true causality is the explanation. Not some sort of general hand wavey kind of thing, but actual tight correlations. That combined with the fact that the condition manifests itself around the time that vaccination is being done on all sorts of "long believed to be involved in" is pretty much a given.
Now that autism is getting greater attention, among the things out there are early recognition, and with staggering frequency, BEFORE vaccinations.