I'm not saying false allegations are NEVER made but I'm willing to bet they're extremely rare particularly given the known stats on dv alone and other abuse (EA, financial, sexual coercion) is much harder to prove.
My life experience has been that many of the men who CLAIM they are being prevented from seeing their kids are outright lying - we saw that with fathers for justice.
My ex tells people I stopped him seeing dd and that he was a fine upstanding example of a father. The truth is even when we (dd and I) were still in walking distance he couldn't bother his arse to walk 10 minutes, he'd turn up drunk and belligerent to take care of a 2 year old? As she got older he continued to cancel last minute, requested swaps constantly, didn't do anything with her when he did have her (didn't find that out till she was older), didn't listen to her or take an interest. We moved back "home" to my parents town which he kicked off about, but he didn't appreciate that I'd no support network in the town we were in when we split and he'd no ties there either and could be posted any time and indeed was just a few months later to somewhere that was actually easier to travel to from where I moved to, if I'd stayed put it would have been murder! I bent over backwards and organised, paid for and did the travel for her to go and stay with him for large parts of the school holidays, during which she was largely ignored and only given the same amount to eat and drink as her much younger half siblings resulting in her losing weight when with him which she could ill afford. As she got older (but not old enough - not yet 12) she was used as a babysitter for the younger ones too.
When dd discovered all I was doing to facilitate her visits to her dad in her early teens she asked me to stop. She wanted to see if he'd make the effort. She'd also always been the one to call/text him to this point and she took a step back on that too to see what would happen. What happened was...nothing. He didn't call or text, he didn't ask me after her, he made no arrangements to see her didn't even ask for school holiday dates. I gave in the first couple holidays and made last min arrangements but it was expensive and awkward and dd was miserable. He hasn't seen her now in 6 years - purely cos he can't be arsed to organise himself.
He refused to pay any maintenance until csa finally caught up with him (was in a well paid regular job - army), even when they did he fought it all the way. Begrudged every penny even though the amount calculated was nowhere near half the costs of raising her even on my limited budget.
Even birthday and Christmas she'd get only token gifts while her half siblings were getting games consoles and designer clothes galore. I'd have sucked up the lack of maintenance if he'd at least treated her fairly on things that instead made it obvious to her that she was seen as inferior.
Try explaining to an 8 year old girl who's visited her dad and his family and seen that her half siblings ALL (3 of them at the time) individually got their own games console and designer clothes and other expensive gifts when all she's been given is a hand me down knackered mobile phone and primark clothes, that her dad doesn't hate her!
He's blamed me plenty of times, said I turned her against him. I wouldn't do that but even so I didn't need to be was perfectly capable of doing it himself and he succeeded.
I'm also minded of the other separated parents I know and very few of them the dad has played fair, sees the kids a reasonable amount of time, gives them quality attention in that time and pays maintenance without quibble. In fact out of over 40 I can count them on 1 hand! That's men of all ages and backgrounds.
The only men I know who have been actively prevented from seeing their kids are abusers - proven in court - but they lie to those who weren't around at that time. It's all lies - yea cos people get convicted on no evidence all the time 🙄
That's another thing we saw with fathers for justice too men who claimed they were being unfairly kept from their kids when they were violent thugs not allowed to see their kids as they were a danger to them.
So no, I don't believe the majority of these men bemoaning their situation on that site are genuinely hard done by.