Composite Shims & Liquid Nails
I received replies from both companies. 

Liquid Nails wrote, "They will not react per say but there is a good chance they will not adhere properly. Unfortunately there is nothing that we can recommend for HDPE because nothing will adhere."

True Line Mold, the manufacturers of Timberwolf Composite Shims replied, "What we have found with Liquid Nails and Elmers Glue-All Max is that they will adhere to the shims, but require a longer cure time to completely set-up. Thus why I believe the Liquid Nails states not recommended for use with plastic, vinyl or composite lumber because most applications do not allow for an extended cure time. You should not see any degradation in the shims, it may simply be a case of the adhesive not being as strong of a bond as you desire provided on the cure time."