DiplomatObvious loophole of not breaking if attacked is obvious, so not going to comment on that.
What else does this feat do, what is this supernatural ability they have?
Advantage on future Social Checks.
That’s it, that is all Diplomat can give you once the attack loophole is closed. It says nothing about being a friendly acquaintance, all it does is charm and all charm does is prevent the target from attacking you and give you advantage on social checks against the target. And, once you have that advantage, you are using normal skill rules to accomplish whatever your plan was, and so things are back in the DMs court.
Menacing
This one has more potential to be aggravating, but there are a lot of factors at play.
The target has to be within 30ft to be scared, so if they run and you can’t follow, they can break the chain, if you can’t use you attack to scare them, they break the chain and reach you.
If you are in melee with the target it can break down to 1 attack to give the enemy disadvantage on all their attacks. Good, but not gamebreaking against a single foe most of the time.
Only working against humanoids means a few things. But the big one is their equipment. From the MM most of the enemies don’t have good armor, and don’t have the listed ranged equipment they might have. But, they are intelligent humanoids, so they can change that. It isn’t that big of a leap to assume most raiding type humanoids carry bows, or that they have 4-6 spears or handaxes for throwing. So, begin thinking about what extra weapons it makes sense for them to carry. Gnolls for example, already wield spears, and maybe they like to impale people on walls and leave them there, or in RL spears could break so they carry extras, nothing states their full equipment load out, so we have some wiggle room.
But, from previous conversations, I think your biggest issue is that they can use a non-magical ability to scare a guy you think should be fearless, but not immune to fear.
I can’t help you there.
Personally, I would follow my gut, depending on the situation, the enemy, the roll, and the table. Most likely, I would just let the enemy be frightened. They are mortal, they can feel fear, if they cannot feel fear I would make them immune to fear, even magical fear.
The ability does, by RAW, take away your ability to tell the player no, you are not scary enough to scare this guy. And, I find that fine. I’ve rarely had a PC invest in intimidation, and if someone did to the degree of getting this feat on top of it, I would have to re-evulate how scary they actually can be. There are abilities in the game that just do things, whether or not the DM wants them to happen. This is one of them, and I’ll work around it if I have to, but I don’t see it as breaking something essential in the game.
Stealthy I think would also be fine with a few common sense tweaks, namely that it fails to work if something is looking directly in your direction as you move. If the creature who could spot you is otherwise distracted (such as being engaged in combat with another creature) the feat works without breaking verisimilitude. The feat, to me, implies the PC is capable of sensing and making the most of momentary distractions (it's not hard to cover 10 feet in a split second, which is all the distraction a master sneak should need to move from cover to cover). It just breaks down if the subject is staring directly in the space your moving through for the entire time with nothing else to serve as a distraction.
Would not already allow a player to move 10 ft through an open area without breaking stealth if the enemy was distracted? I mean, I’m not going to be looking down the empty hallway if an orc is swinging an axe at my face. And if my passive perception is 13 and the rogue rolled a 22, I think that should be the end of that.
It is nearly supernatural in effect, but the number of times I could see it making the difference to allow the player to do something they could not already find a way to do, is pretty low.
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