When only lightly obscured, yes in my opinion, unless you're a wood elf, skulker, or level 10 ranger, or the observer is distracted in some way. It has come to my attention in the course of this thread that this is different from 4th Edition, with which I have very little familiarity, especially when it comes to the mechanics.
In 5th Edition, cover of whatever degree, provided by an obstacle, only affects such things as targeting, AC, and saves. It has no mechanical effect on vision. An obstruction, however, blocks vision, and whether it is of sufficient size to hide behind is left to be determined by the DM and has no relationship with the degree of cover afforded. Personally, I require an obstruction to be at least 5 feet wide for small and medium characters to hide behind, and at least 10 feet wide to become hidden if they are observed going behind it, to create enough uncertainty about their actual location. I think in most cases this would grant the hider total cover, but I don't consider degree of cover as a circumstance for hiding.
And this describes exactly the problem that I have with the rules or how those rules are parsed:
The rules are there to help determine whether somebody can hide in that brush. If I'm an elf in my FR campaign, it doesn't make a difference whether it's 1987, 1996, 2003, 2008, or today, either you can or you can't. For something mundane like hiding (to start with), you figure out what's possible, and then the rules should support that.
Personally, I think the 5th edition rules support hiding very well, although it's clear that our own personal experiences will color what we think is possible or not (from mundane hiding).
When 2.5e came out (really it started with AD&D, and even earlier in Dragon Magazine, although it often had more clarification about the intent of the rules), by spelling out the rules in "better" detail, it sparks arguments about the wording of such rule. The English language is a very imperfect thing (Lawyers make millions because of it).
A hunter often hides in light brush in wait to surprise their quarry, in exactly the same way my lack of observation surprised me when I saw the bear. (Although in that case there really wasn't any obstruction between us. I can only guess that it was hidden behind a tree when I walked by and I didn't look in its direction). It's very possible to hide. There are degrees of how easy it is to hide. For example, could you hide from a blind man if you were in light brush? Not very hard. What about from a deer or bear? I'd say yes, people do it all the time. The same creatures if you're upwind? Maybe not. They might not figure out where you are, but they'll know you are near and leave.
Now from an orc, or human? Human baby? All of these change the likelihood of success in some way or another. So the question becomes first, is it possible at all, under ideal circumstances; such as the target not seeing you enter the brush?.
If the answer is yes, then you start there. You can make the attempt. OK, so you're being chased by somebody through the woods. Their only focus is you, and not tripping or getting hit by branches in the face. In that case I'd say the circumstances make it easier to detect you, so they get advantage. Has it altered your ability to hide? Not really, the circumstances changed in a way that makes it easier for them to know where you are, rather than harder for you to hide.
Now you're running through the woods and there's a light snow on the ground. In that case I'd say the circumstances make it harder for you to hide, so you have disadvantage.
Personally, I also don't have a problem ruling that in many circumstances it's not only harder to hide, but easier to find you. IN which case they would have advantage, and you disadvantage. Is this stacking? The effect of the rolls is in a way, but it's not much difference than a few abilities or feats that give you a -10 penalty to get a bonus to do something.
To put it a different way, in light snow, you run through the brush and around a tree. The target is following you, but there are breaks in their vision as they look at their footing, trees obscure you, etc. So I think the possibility still exists, but it would be very, very hard.
So now what about in combat? I get why the rules state that everybody is looking everywhere, but that's really not entirely true. Sure, you'll be keeping your eye out for danger, but most of your focus is on the most immediate threat. So what does that tell me? No, we don't need more complicated rules about facing and things like that. Instead, it opens up opportunities. Like the rogue can attempt to hide. There may be modifiers. One of those modifiers might be your ally using the Help action to make a Deception check to keep the attention of the target away from the rogue, so they can hide.
Again, 5e supports this approach much cleaner than almost any other edition - Is it possible? If yes, is there advantage/disadvantage. If the modifiers aren't enough to be +/-5 then they aren't really worth considering.
Also, the way I use Perception (or any skill) is much like a take 20. If their Perception gives them the ability (that is they can "roll" high enough, whether passive or not, then they will eventually find you. If you've successfully hidden, then move again, you'll need to make another hide check. If you're hiding behind a wall, and their actions bring them around to where they can see you, they don't need to make a check, they've found you.
Now, if we decide that an elf is better at it than other creatures, I would recommend granting them expertise in it. My expertise is +2 with a max proficiency bonus of +6 (the best at what they do), not double proficiency. But it basically tells you it's still a mundane ability, but they are really good at it. Whichever form of expertise you use, at 1st level they are the equivalent of a 9th level character. At 5th level they are the same as a 17th level character (RAW), or a 13th level character (my way).
So now the 1st level elf isn't magical, it's just better. Would a (highly trained) 9th level character be better at hiding from a 1st level character? I think so. Is it magical? No, just better.
The most important point though, as far as I'm concerned, is you look at the circumstances first, and the rules should support it. Many gamers (especially some min/maxers and rules lawyers) look at it the opposite way, what do the rules allow me to do, even if it doesn't make sense? Like the Kobold Ballista.
