What link does the priest have to the school? Is he on SLT or teaching at all? Or does he just provide pastoral care and sit on the governors? If the latter then I doubt he really has much influence, so I wouldn't worry about it one way or the other.
At primary school I would be surprised if they mentioned much if anything about sexual ethics. However, you need to be aware that the Catholic Church is anti-abortion and anti homosexual practice (how much this translates to homophobic treatment of gay people is much more varied). I'm neither defending nor criticising that (although I do have opinions on it, they're not what's at stake here), but it's a fact that a Catholic school will be expected to adhere to Catholic teachings on those matters, as on others. If you strongly disagree with them, then maybe a Catholic school isn't the best choice. OTOH, as I said, I would be very surprised at primary level if these things came up often, if at all.
In terms of women in the kitchen, that is not a teaching of the Church and not a view with which most Catholics in the UK would agree (whatever their liberal-conservative tendencies), and since Catholic school teachers don't even have to be Catholic (except the Head, Deputy Head, and Head of RE) and in the vast majority of cases are either non-Catholic or non-practising, I can't see how there's any danger that it would be promoted as an agenda. If it were something coming from the priest (it is possible that he holds such views, although it would strike me as unusual that it would be something he would spend much time talking about, particularly to young children), it almost certainly wouldn't be reiterated by the teaching staff. In a private school, you will tend to have a higher proportion of practising Catholic teachers, but they're nevertheless drawn from the general population (of teachers), so the chances of them being able to employ a team of extreme right-wing bigots, even if they wanted to, are quite slim.
As regards the confessional, the Lent poster etc., I have worked in Catholic schools of varying shades, and such things would be common though not universal, it seems unrelated to the Opus Dei matter.
What I would do, in your shoes, is read through something like the Catechism (you probably wouldn't need all of it - maybe just the bit on the 10 Commandments). It's available free online. Obviously there will be teachings you disagree with, otherwise you would be Catholic, but if there's stuff which makes you think 'this is horrendous, I can't stand the thought of my dcs being taught that', then maybe reconsider the Catholic school idea?
If it's an actual Opus Dei run school, or they have some more serious involvement with it, then I would be a bit more wary. Not that anything seriously cultish/masonic etc. would be going on, but just that they will be properly hardcore traditional Catholic and push the conservative moral teachings, which might not be what you're looking for. Opus Dei are quite strongly orientated around the 'traditional' family (they are 98% lay people), so in addition I would expect there to be serious expectations of parents of the school to get involved with things, which you might not be comfotable with.