Eating before early workout???

Unless you're a professional athlete meal timing is not relevant.

I work out before breakfast (cardio and weightlifting) and it makes no difference, it's just personal preference.

Here's a handy diagram

My question is how crucial is it to eat before a workout?
It isn't at all unless you are going hard for two hours or more. It helps some people perform/feel better - for others it's the opposite.

I'm someone who wakes up at 6 and heads straight to the gym so I'm not really hungry before the workout.
Save your calorie allowance for when you are hungry.

I've read that workout out fasted will deplete your glycogen stores and in turn make you lose muscle. I've also heard that a fasted workout can help you lose fat.
All these points are nonsense.
Glycogen and fat are used consecutively not sequentially.
You have really large stores of glycogen (perhaps more than 2000 cals worth for you), delaying breakfast is an irrelevance.
You don't lose muscle by using it - you lose it by not using your muscles.
If you did manage to use up all your glycogen you would be unable to exercise - bonking or hitting the wall is an awful experience (crushing fatigue, mental confusion.....).
Your fat loss is a result of a sustained calorie deficit over an extended period of time and that's predominately down to eating the right amount - when you eat that amount only significantly matters for adherence.