When a grease is mixed with another, the result is almost always softening of the grease. In rare cases, the grease can harden. In your case, just stick with one grease type and regrease a little more often than usual. You wont have a failure in your kind of application.
So in summary, dont mix greases if you can help it. In your case, just use your new grease from now on. You'll be fine. You may notice grease dripping off your grease points.
OBTW, in a roller bearing application, the grease can soften and run away from the metallic parts. That is a bad situation and can cause a bearing failure.
dwight