Bought a little 4oz. bottle of Mopar sure-grip additive. Was going to buy some redline 75w-90. Lucas or royal purple75w-90. My question is should I use synthetic. Will it work with the mopar additive or not. Or do I find a non synthetic 75w-90???

The sure grip additive should work fine with synthetic. FWIW I use the GM spec stuff sold by AZ with both synthetic and standard lube.

If you are running older seals in the rear, it may prefer conventional lube. Synthetic is nice for really cold running (eg below zero) or continuous hard running hot (eg. road race using xxW/140).

If you are not doing the above, suggest standard 80W/90 plus your additive to reduce chance of leaks... and save your money.

I use the Redline gear oil, and have not needed to add any additive.
http://www.redlineoil.com/content/files/tech/Gear%20Oil%20Tech%20Info.pdf

From the link above:

LIMITED-SLIP COMPATIBILITY
Red Line Gear Oils, with the exception of the
75W90NS, and 75W140NS, already contain friction
modifier required for operation in limited-slip differentials.
Additional additive is not usually required, but
newer units or those with more lockup capability may
require 1-4% additional Red Line Limited-Slip Friction
Modifier. If Red Line is not available, the manufacturers
recommended friciton modifier is compatible. Do not
add addtional modifier unless necessary, as too much
will result in excessive wheel spin. To perfectly tune a
differential, start with the 75W90 NS or 75W140 NS and
add the Red Line Limited-Slip Friciton Modifier until the
limited-slip chattering just disappears.

PRODUCT APPLICATION
75W90 Gear Oil - the preferred product in nearly all car
and light truck differentials, both conventional and limited-slip.
75W90 is preferred for most racing applications.
It contains friction modifier which is recommended for
limited-slip units.

75W90 NS, 75W140NS <-- The "NS" oil does not have the friction modifier.

FWIW I have tried "limited slip ready" lubes a couple of times without additive. Most recently Mobile 1 xxw/140 synthetic. The bottle clearly claimed "limited slip ready, no additive required".

After some driving it started catching and making noise. I sucked a little lube out and added the friction modifier and it was fixed. Regardless what the label says, I think they need the additive, at least with a clutch type sure grip.

Thanks I will find a 80w-90 non synthetic throw in the additive and burn rubber.