The grinny face was to imply tongue in cheek humor. I was just ribbing you a little, not calling you an idiot.
If both wheels are spinning with the brake applied, then no, you're not burning up your clutch plates in the differential. It's when you are doing the one wheel burnout. If both wheels spin on a regular acceleration burnout, I wouldn't worry about it. That means your differential is working.
Here's the scenario as to why it was working like you wanted it to before and why it isn't now. To install the differential, you probably had to loosen the drums some to get them off. In the process of putting them back on, they had to be tightened back up. This readjusted your rear brakes so they would work the way they are supposed to. They're called limited slip differentials, not no-slip differentials. If they didn't slip, you wouldn't be able to turn.
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351W 89 Mustang GT Convertible