So, we bring this around to the DM allowing or disallowing something. Now, the game is more balanced with the idea that everything that is written will work in a traditional, generic, D&D game. Before this wasn't really the case. Especially in 2E there was an arms race going on. Things would be unbalanced and it was the DM's job to adjudicate things so that his game stayed balanced if that's what he wanted. The idea wasn't to allow things, it was to disallow things. A DM had to disallow things or his game would soon spiral out of control.
That isn't the case anymore. You can play a vampire fiendsh half-dragon PC in a game and it won't be unbalanced, it will probably be weak. So, now the DM disallows this only if it won't fit his campaign. Before the DM would disallow it if it wouldn't fit the campaign or because of a rules consideration (unbalancedness for one). So, now the DM has half the reason to disallow it.