Have a look and the senior staff names (often available on the website and see if they have social media and check it. Also look on the website for key groups for parents PTA that sort of thing and look at the social media of those parents.
Does the school social media drape itself in flags for the various days, months etc to the exclusion of all the other groups?
Look at the displays on the walls especially in English, history, sociology, politics and even RE classrooms - are there other political beliefs on the walls? - BLM/white privilege etc., with no balancing view suggests generally wokery and staff allowed to teach their politics without hindrance from the leadership. Do they use the words women and girls a lot?
What about science - do biology displays look like they did when you were at school or have they erased women and taken on gender neutral language?
Which books are displayed prominently in the library? Are there political groupings of books? Have they hidden JKR? Is there a feminism section in the older students library and is it just Caitlin Moran is is there a wider range?
Are there posters saying 'be kind' or that hate will not be tolerated (why does that need saying? are they begging the kids to be hateful???) because that suggests a strong identity politics view.
Go in the toilets - you should see the layout with regard to boys / girls. No good if single sex loo is on fourth floor but there are unisex loos everywhere else! No time to go at break. Ask the kids - is there time for the loo at break or between lessons, that might reveal a problem. But also look at the walls and back of loo cubical doors: last school toilet I went in had loads of posters about 'people' checking their breasts for lumps.
Is there an LGBT group? (ask if the clubs are all sports or academic or is there any thing else? That will probably get the answer without you asking directly).
Where do they get their PSHE resources from? Are they written in house or do they buy a scheme in and if so from where? Are they on the school website?
If you are shown round by kids, ask the kids if they have debates and discussions and what on? Do they enjoy them? Have they ever had a discussion that changed their mind about something? Just ask them open questions but the kids might reveal the prejudices of some departments or staff without realising it.
Age of the staff. More middle aged staff members usually mean less wokery.
At open evening they won't know who you are and won't be able to identify your child probably. Many schools have two nights: go round with your child on one evening and round on your own the next and ask the questions then if you really want to keep your child out of it.
There will be loads of clues if you start looking at you go round though - they can't help but give themselves away!
(I'm an ex-teacher, DH is a teacher - he says anyone going round his school would know because of the wall displays)