The difference comes with our defintion of 'woke' - which I'm reliably informed by Americans means something different in the US than it does in the UK.
The article is designed to get people to concentrate on what they're actually arguing for or against. Being 'woke' and being a classic liberal (like me) are different positions and slowly and have been slowly divorcing themselves for the last few years.
A classic liberal position would say that people can exist in society provided they do no harm to others. This means that paedophila (as a sexuality) should be accepted, because in and of itself, it does no harm. I would prefer to live in a society that showed compassion to those people and find proactive ways to make their lives easier and keep children safer. As you've pointed out, there are many people who have complicated reasons for this sexual preference.
Making the classic liberal position valid is the leap you have to make between the state of being and the state of doing. It's a complicated one and requires careful analytical thought. Paedophiles aren't bad people, they're inclined to do bad things - and we should judge the situation on an individual by individual basis.
Many people who rush into arguments from a 'woke' position fail to think deeply. They see the world comprising of oppressors and the oppressed. They can be easily manipulated into fighting for 'the underdog' without considering the implications of such a thing. 'Woke' people, who don't ground their reasoning in classic liberalism are problematic. They become moral relativists. They don't have a fixed position and they want to be 'the good guy' - this comes with a huge load of problems - because being the good guy isn't quite that simple.
If you want a concrete example - then I recommend reading about Keira Bell here in the UK. Her high court battle is leading to all sorts of problems. These issues are complicated, compassion is necessary, but there is nothing compassionate about a world view which polices tolerance with rampant intolerance.
My ideological mission on Medium, if I could define it, is to allow people to see the difference between classic liberals - who believe in a tolerant, open and fair society - and woke-liberals who believe in enforcing such a society along lines of their own choosing. The first position is broadly centrist, the latter position looks left wing but is actually a right-wing position, arguing for the niche interests of protected groups above others. Classic liberalism is how I think a fair society gets built, this new form of modern liberalism is how I think society descends into acrimonious in-fighting.
This was a good discussion and I enjoyed it. Your compassionate world view does you credit :o)