On the one hand, Wakefield's studies have been repeated umpteen times and none of his results have been replicated, indicating that his results weren't as accurate as he thought they were, plus his control group (was it 12 children?) was laughably small.
Documents that claim to show proof of a MMR/autism link have been debunked and proved not to be right (eg, there was believed to be a link for black boys in a certain area in America, this was since found to be false and to do with a vaccine program that was introduced, and these children first had contact with HCPs where before they had none, so their ASD was first highlighted at a time when it looked like it corresponded with their vaccinations).
I was struck by the lack of appropriately experienced Drs in vaxxed, claims were made but never backed up, no evidence of anything is given, just lots of dramatic claims designed to capture the unquestioning mind, I guess this has been ok because the film isn't a bona fide medical advisory documentary, it appears to be badly put together and relates to medical issues in a fictional way that suits Wakefield's agenda. Had the film been made with Drs fully experienced with ASD, neurology, vaccination specialists etc, it may have held more credibility, but it didn't, which to me speaks volumes. It's rather like watching Most Haunted and seeing it as absolute proof of ghosts existing.
On the other hand, for some parents, an autism diagnosis for their child feels terrible, the worst thing in the world - usually because of information from the experts, and other people surrounding them, and (in a completely anecdotal way), I've noticed this attitude where ABA (a form of therapy which is considered abusive by autistic adults who have been through it) is commonplace, so there is obviously devastation that a child is autistic and a need to train the child to behave in a non-autistic way and a desire to cure them.
It's a common thing with any diagnosis to look for answers, look for a blame. MMR is an obvious one, but one that has been disproved over and over again. As is seen so often though, should a parent worry about it, they are generally treated as stupid by the pro-vaccination community, and discussion cannot take place. I believe this is the kind of scenario that benefits charlatans like Wakefield, because he appears to be doing something that many other Drs are not doing, he (and others like him - bleach enemas anyone?) is listening to them and answering their questions, and not treating them like a bunch of tossers, and he's drawing them right into his agenda at a point where these parents are vulnerable.
Support for DC with ASD and treatment of parents by experts is notoriously poor, and I think this leads parents to believe the charlatans and put their trust in them because they don't feel they have any other way of getting through their lives.
There's also the fact that autism awareness/acceptance is piss poor and leads to many parents feeling isolated and wanting to fix their child, rather than being able to understand that they're not broken, just needing a different approach, one that suits them better.
So, no I don't believe that vaccines are linked to autism, but I can see why so many buy into that belief.
I'll also add that I was diagnosed with ASD last year, aged 40. When I was young I was still autistic, but the diagnostic manuals then we're still works in progress, as they still are today.
OP, if you're interested, have a read of Neurotribes by Steve Silberman, it's excellent, and unlike Wakefield's agenda of ASD = worse than death, it's actually very positive about autism and gives a good history and explanations as to the higher diagnosis levels today.