Logs:

Steps to Reproduce:
Just launch the game with those two
Description of issue:
Most of dragon eggs disappear from creative menu, and the dragons themselves with player becomes invisible after taming and restarting the game. With invisible, I mean; the models are gone. I remeber it almost always ends like this but I remember the case when once the models worked but I dont remeber what I had done diffrently

I cannot seem to reproduce this issue with DML and ModernFix alone, as per your steps. Though, the information here is lacking, like your game version, so I assumed latest version. Do you have any more parameters to this that I can use to try and reproduce the issue here?

I created a modpack that has ModernFix in it. I am trying to incorporate Dragon Mounts Legacy.

I seem to be having the same problem, or maybe a similar problem. In JEI/Creative Menu all I can see is the Aether Dragon Spawn egg, and Aether Dragon Egg:

When I disable Modern Fix and load back in, now all I see is the Water Dragon Egg. LOL

I apparently have another conflict going on as well.

This is all on Forge 1.19.2 // the modpack exists on Curseforge and is called Plastek so you an see the modlist

This is just a quirk of how the eggs are added in the game, and not of modernfix's fault.

Dragon mounts technically only registeres one dragon egg and one spawn egg, and they work off of all of the breeds.

This is due to the fact that items and blocks in minecraft are still statically registered, while the breeds are dynamically registered.