Seen the film twice now. There is nothing offensive in it. None of the family are shown to be nasty. The parents row off-screen, but there is no implication of anything other than straight-forward discord between them. The siblings squabble a bit; Dad tells Steven to get a job. Mum encourages him to follow his dreams; sister takes the mick a bit, he takes the mick back. Nobody is made to look abusive or cruel.
If the family are genuinely offended, it must be from some sort of wounding feeling of having any portrayal whatsoever of their domestic life, because the film's content doesn't merit the tone of Jacqueline's statement. But I'd be amazed that they hadn't complained like this before; years ago, nearer the time, with previous discussions or mentions in books etc, let alone Morrissey's lyrics.
The film was a low-budget indie effort made by lifelong, Mancunian fans of The Smiths, with nothing to gain from alienating themselves from something they love so dearly. Numerous interviews with the cast and director mention the small bugdet, short timeframe and logistical constraints, meaning certain topics (e.g.: vegetarianism, trips to America) were left out, in favour of trying to tell a simple story about a young guy. Without millions to spend on an exhaustive 8-hour drama epic that captures every facet of his pre-Smiths life, what can people reasonably expect from one film? The thing is, most fans probably wanted to see a visual, cinematic realisation of the same emotions they had when they got into the band, or maybe a journey that mirrored their own growing up, and that is basically impossible.
Also: not seeing it 'on principle' is totally ridiculous. It's just a film; it's not someone waging war on anyone's personality or beliefs. The statement is way over the top, as was James Maker's (whose was very funny), which was only based on the trailer, not the film. Enjoy it or don't, but it's not to be taken so seriously.