Outsiders does not cause the target to lose Ranged Combat Expert, just the +2.
They would still be able to use trick shot.

It cuts the RCE off.....Therefore they would not be able to use trickshot.....

Can you please point me to what you used to base that on?

It does not cut RCE off.
True, Outsiders prevents a figure from getting the +2 damage from RCE, but RCE is still present on the dial, and therefore the character still meets the prerequisites for Trick Shot.
It's really no different than when you make a Running Shot with Trick Shot - You cannot use RCE when doing a RS, but it's still there on the dial and therefore Trick Shot can be used.

Also you don't even need to have Ranged Combat Expert to use Trick Shot. It is only one of the possible prerequisites.