I'm in two minds about this.
On the one hand, as a former civil servant I've been horrified by how captured and in thrall to gender ideology the civil service has become. As @FarriersGirl has said, the way this has played out is completely at odds with the value of 'impartiality' that is at the heart of what it means to be a civil servant in the UK.
On the other hand, Pride used to be about acknowledging that LGB people should not be ashamed of (and indeed should be proud of) their sexual orientation and I would not want to see any challenge condemning that as a legitimate thing for civil servants to support.
If the challengers are focused on the way in which T activists are undermining women's rights (and reality), then they have my support. If they are also targeting LGB activists arguing for a level playing field, then I would be less keen.