The Alpha course very much depends on the church and the people that are running it. There are CofE churches that are more liberal, more ‘high church’, more evangelical etc.
There’s an evangelical church by us I’d be upset if a close member was attending an Alpha course at, because they believe in creationism, msn as head of house/woman as head of home, aren’t progressive on LGBT issues (love the sinner not the sin - which is extremely problematic) and have links with US far-right churches. They’d come under CofE. On the surface they’re very ‘modern’ - it’s all Instagram and video link worship with rock music and a thriving social community of young people - but actually they’re extremely traditional in attitudes and backward, if you ask me.
OTOH, if someone was attending the Alpha course at the more ‘traditional’ CofE church up the road, with its coffee mornings fir the older generation and Sunday school crafts, I’d feel happier as I know the vicar is - whilst appearing to be old school as that’s the building/community he’s in - actually a really liberal, forward-thinking bloke.
What you describe would worry me. She can’t remain in a relationship with a man like you’re describing without ‘converting’ - the pressure will be huge. I’m a believer married to a non-believer and we navigate that fine, but I’m not so invested in my faith being a fundamental part of my whole life and community and attitude in the same way you’re describing this bloke’s family and life.
Look out for her, but be careful to be supportive no matter what. If you alienate her by saying her new exploration of faith is wrong or the church her boyfriend is from is wrong she won’t be able to come to you if she’s having doubts.