School flying the trans/pride flag...

That's a gender critical opinion also held by the gay community.

Fixed it for you.

"which I think is a deeply homophobic ideology"

That's a gender critical opinion and not one held by the gay community.

Article is two years old, but makes some very valid points:
https://archive.ph/po0cO#selection-1531.0-1545.477

'The annual rainbow-fest of Gay Pride is here, but instead of the long-established six-coloured flag, with colours standing for broadly positive and inclusive values like “life” and “healing”, we once again see the new “Progress Pride Flag” everywhere from branded electric bikes to bank branches.
The Progress version emerged out of identitarian leftist campaigning in 2018. It sports pink and blue lines for “trans pride”, black and brown for, you know, all “black and brown” people and, on some, a purple circle on yellow for intersex people. It signifies a constantly changing game of progressive one-upmanship and inclusivity bingo. Opt out and, to the new left, you’re fair game. So when I see the Progress flag, I don’t think of “pride”. I feel confronted by a toxic ideology of reductive identity politics and oppression hierarchies.
For this good reason it is illegal to fly it on government buildings without planning permission. Yet it has appeared over both the Foreign Office and the Bank of England in recent years. Private companies can do what they like, but what on earth are venerable state bodies playing at by displaying this highly controversial, political symbol? And who gave permission — if they did? The worst of it is that the culprits almost certainly don’t even realise that it is political.'