Hey Luke! I have not tested Old School Stylish with the OSE Advanced Fantasy races, but I will note that the race/class divide will tend to make slightly stronger characters overall. As the OSE base classes don't get weaker if you add in the extra features from the Advance Fantasy races, all characters basically get a few extra features.
Personally, I don't think this is going to substantially diminish the challenge of an old school game. A dwarf's (possible) bonus to resisting poison probably won't encourage a player to drink suspicious liquids left and right, and an elf's ability to detect hidden doors doesn't happen often enough to preclude players prodding around dungeon rooms just to be sure. And on top of it all, none of the Advanced Fantasy races do much to mitigate the fact that your characters probably have little enough HP at levels 1-3 that they could be killed by a bad round in combat at pretty much any time. These abilities will give your players a little bit of a cushion, but I don't think they will qualitatively change play. Overall, if your concern is about power scale, I don't think you will be unhappy using the Advanced Fantasy races. Just be sure to use the rule that gives humans abilities too, as the racial class limitations are obviously not going to apply when using this supplement.
My recommendation: if you want to keep things simple, let players say their character is whatever they want and pick a single racial ability from any of the OSE Advanced Fantasy races to describe their choice (with the onus being on the player to justify it). So one player with a human character may take sleep immunity and say they're an insomniac, and a player with an elf may take leadership to reflect their natural talents. But that's just me -- I like to keep fantasy species stuff as simple as possible.
That said, this is just my prediction. The only way to really find out is to give it a shot! Please let me know if you have any feedback after going in whatever direction you choose, and thanks for your comment!