So it was recently brought to my attention that because the dragons breath isn't stated it's a magical effect it doesn't feel magical damage.

When I looked at it, it made sense to me. To my understanding magical damage has to come from a spell, magic item, or expressly stated as such.

Examples are: the spell fireball, +1 weapons (or common magic items like the moon touched blade/unbreakable arrows (because they are magic items)), or the monk feature that turns their fists into magic damage.

Since a dragons breath had none of these stated I have to conclude that a dragons breath weapon isn't magical damage. To further emphasize this, a dragon is able to use it's breath weapon in an anti-magic zone.

So I was wondering what are other similar effects?

I don't mind the change when it comes to dragon breath weapons personally, because just because a creature is a magical breast didn't mean all is smilies are magical.

Yes in 3.5 it was nice to say it's a super natural ability, but that still doesn't mean it's magical too me.

For instance, if I wanted a world of low magic I could make the dragons "function" like how I believe it's explained in the movie Rain of Fire, a biological function.

I know I can as a DM say the breath weapon is magic damage (out effect).

Although the gaze attacks/effect bother me a little. I haven't gone and read any of them, but I feel if it turns you into stone, that's magic. If it only stuns or paralyze you, then that could just a fear effect, which doesn't necessarily mean magic.

But going back to breath weapons, like a gorgon (which I hate that name for it because that what Medusa is, a gorgon) that one turns you to stone, so I feel like it should be magic.

Every dragon I've used recently (currently running a campaign were I've been sending young and adult dragons at my players for trials in the dungeon they are in) have had a second type of breath weapon, like sleep gas, paralyzing gas, and the like. 

(At the time) not knowing that breath weapons weren't magical effects mechanically, I have a Warforge in the party, assumed he was immuned to the sleep gas. Later he failed the save for the paralyzing effect and so was affected by that. And I've also had to rule that the gas effect anyone (other than the dragon who did the breath) is affected by the gas even though they might not breath themselves (again the Warforge).

Yeah... Just like how Adamantine armor is magical but per XGtE Adamantine weapons aren't. Just a special marital like they were in previous editions.

Part of my problem was that I also had to other players who have an ability that lets then hold their breath for over an hour (Air Genasi and Vedalken). So if I had the Warforge not be affected because he didn't need to breath, I'd have those two meta game and use that ability to also not get affected.

So if and when I find things I try to make them consistent across the board. It's already hard enough to kill them,I constantly have to throw deadly encounters at then just to challenge them in a fight... Which also means to my dice deciding to hate one person in particular and down them often in one blow

Holding your breath doesn't do anything against an effect unless the effect specifically states so. Look at the spell Stinking Cloud as a reference. 

Quote from Lyxen >>

I know, it's a bit confusing and, although I like Eberron and the concept of the Warforged, they have always been a huge pain in terms of mechanics, as it does not really make sense to have a machine that works exactly like an organic being. And again, 5e is simplified, which is good, but as the consequence the Warforged, technically, behave even less like machines than in the previous editions. I know that the game balance is at the core of it but the result is something that is not very satisfying.

 This  ^^^ .