I think even if I'm "probably" planning to go wide with Liberty or even go on the attack with Honour, I would be most likely to take the Tradition opener if it was truly blind. The extra early speed for policy generation will have petered out and started hindering well before finishing any of the trees, but it's enough to still carry you to the free settler or the GG and the discipline boost - maybe a bit slower but not enough to worry about too much (someone could probably do the maths with Liberty), and the extra border growth is always nice. Plus you can delay monument much longer which speeds up workers or archers etc. And if you don't continue with Tradition, you can always take Legalism later for some free buildings. So it's definitely the "safest" of the three openers in that it hurts you the least if you choose wrong.
If my capital is a rotten site, I'd go straight to Liberty or Honour.
If I meet someone else within the very early turns, that suggests they're close enough to be an early opportunity/threat, so I would probably proceed with any plans I had to go Honour.
If I've already scouted out enough good land for maybe two more good cities, I would still go for Liberty. That's enough for the settler policy to still be totally worthwhile, I think.
If I've built a monument or am close to finishing a monument, I would go with whichever tree I was initially planning for.