I was told that I am part warrior angel/part fae, but I truly do not believe much in it

As I understand it, fae folk originate from an alternate realm, and some choose to reincarnate on our plane to have a human experience and learn/achieve soul growth the same as those not from the fae realm do. So we as reincarnated humans on the earth plane may have originated from the fae realm and are here in human bodies. While fairies do very much exist, and do appear to and even guide some humans, the don’t manifest as humans in a physical way. Meaning, you won’t see any human sized people walking around with “elf ears” due to being a fairy, but more likely due to a unique physical feature (whether cosmetically engineered or via physical abnormality.) This is what I’ve learned from reading on the subject of fairies, and my own personal experiences.
But I realize and deduce from the spirit of your comment that perhaps you’ll have to warm up to the idea, I know I did. But hey, being open and acknowledging just how much we don’t know is the mark of being wise, no?

Without a doubt there are fae folk among us, and yes there are some who have mixed with mortals.

Its unlikely that any of us are 'part' fae or fairy.
There are elemental earth energies we tend to call fairy or fae, they do not exist in the 3rd dimensional earth though, more like the 4th or 5th dimension.
It's unikely there's cross deminsional breeding, but I could be wrong. If you meet some one who seems to be rather see-through and not fully formed into physicallity and claims to be a fairy half-breed then let me know! I'd love to be wrong about this :)

my assumption is that most humans are "composite" beings, with
genetic material provided from all sorts of various corners of reality.

No matter what we are as a spirit, Fae, angelic, part of a monad, or come from an oversoul as most, part of a soul group, or even part of a logos, when we incarnate, we never become a human, at best we attach to the human system, connect would be maybe a better term, and disconnect from it at the end of it's life.

So, since the Fae and the angelic are not a race they can not interbred.

although "red" and "fragrant" may be unable to breed, we can bring them into union.

An ill conceived comparison.
Lets assume I am an angelic wanderer, in order to come to this planet into the physical realm, I have to attach to a physical body, and with a little skill, the physical body goes along with, what I want it to do.
So, who does the breeding? The physicality or me as the angelic wanderer.
Will the offspring of mine have any angelic part within their physicality?
Of cause not.
Me,as an angelic entity will not leave anything behind once I leave.
This is the rule

rules are made by the rulers, and followed by the followers.

you have determined to leave nothing behind,
does that imply that you'll take nothing away?
(or perhaps the opposite?)
if your visitation provides for no meaningful
interaction, what purpose has been served?

Are you a politician? If not you should become one. You have the ability to use simplified statements and us them as a counter argument.

In the original post the question was raised, are there any half/part faes in here?
My point was, this is not possible, since we never become the human, we attach or connect to the human form and disconnect at the end of the human life, without leaving anything behind, in form of DNA or other physical material.
On a more personal level, whether I ever had a meaningful interaction matters very little to me. I did what I came to do and will leave when the time comes. A bit like a plumper, who comes to your house to fix the pipes, all that matters is if he fixes the pipes, not if you have a meaning full conversation with him. If you have, that would be a bonus.

In regards to rules, as you move on from her, you will find out or rediscover, there are hierarchies on every level of existence, and the form of hierarchy changes on every level, according to the level of consciousness.