Most of the best Belgian beers are "bottle conditioned." This means that the beer hasn't been pasteurised and filtered before it's bottled, so it's still a living thing, not dead like, for example, Newcastle Brown. The reason for this is twofold; first pasteurising beer inevitably has a bad effect on its flavour; that's why Real Ale tastes better than keg. Secondly, because the beer is still alive, it continues to mature in the bottle like a fine wine and can continue to change and improve for many years. This also means that a bottle conditioned beer will still taste superb many years after the pasteurised equivalent has become un-drinkable. It's not just a couple of years either. I bought a bottle of Oud Beersel Geuze in 1999 which had a "best before" date on the label of 2019. (Mind you, it only lasted until about an hour into 2000!)
The natural reaction of the average British drinker is to avoid drinking any beer that isn't perfectly clear. This isn't for any really good reason, but rather because of a number of myths which have become accepted as "common sense".
Myth 2: the sediment's bad for you. If like me you enjoy eating Marmite, then you're already consuming vast amounts of beer sediment, as that most delicious food's main ingredient is yeast recovered from breweries. Indeed, far from being bad for you, there are positive benefits to consuming the yeast; it's an excellent source of many B group vitamins, especially B12 which can be lacking in the diet of vegans.
And No, it doesn't give you the runs!
So should I drink the sediment or not? Different people will find they prefer different beers with or without the sediment. Experiment a bit and see what suits your palate. There's no need to waste money buying one bottle to try without and one with, just pour about ¾ of the bottle into your glass carefully (the waiter will probably do this for you) and when you've drunk most of that, swirl the bottle to loosen the sediment and pour it in. If it turns out that you don't like it, then you haven't wasted much. If you do like it, it will have really been worthwhile.
It's worth keeping a note of which beers you prefer served with or without the sediment, then you can remember for the next time.
Although your tastes will no doubt be different to mine, a few of my sediment preferences amongst some favourite beers include: