I've tried it both ways.
I've had overflows due to overfilling at the start, and by thinking it was safe to top up sooner than it actually was.
If you just let it go, as long as it's pushing stuff out there's not much risk of oxygen/bacteria/insects getting in. But you need to be around to spot when it calms down so you can fit a new airlock immediately. And it can get VERY messy: apart from what you see dribbling down the side of your demi, some very sticky gunk is being carried off by the gas in aerosol form, and settles over a depressingly large area.
If you take some out, you just have the one quick cleanup. And if you're careful and lucky you could save the stuff you took out for topping up, though I don't like to risk infection so I dump it - I suppose you could boil it. If you dumped it, then when you do top up, you have to wonder about how much sugar you lost, how much of the flavour compounds you lost.
I'm retired so am around most of the time, ready to fit a new airlock whenever, so I tend to just let it go - minimal loss of original fermentable fluid. And I can keep the vessels away from other stuff they might spray stickiness onto. But I only get overflow fairly briefly, as it's normally a small error in headspace allowance rather than leaving none at all. If your vessel's full, it'll overflow for quite a long time and make a big mess: in this case I'd definitely take some out.
