Its not really about any vibrations, but more about the load carrying capacity of the central Scherzer's span (The part that is lifted up to let ships pass through) and the general load bearing capacity of the bridge. A WDP4D weighs almost 10 tons more than an ALCO and is about 5 meters longer. This makes it more difficult for the Scherzer span to handle the loco.
The WDP4D locos have a rather high axle load at 20.5 tons. In addition, EMD locos have high tractive efforts (Basically they exert more...
more... force on the track, and pull heavier loads). The bridge was originally designed for MG and was strengthened to handle BG operations, and thus, is quite old. The high tractive effort of the locos means that the bridge will experience heavier loads, which it may not be able to sustain, at this age.
For the same reason, twin ALCOs are/were also not allowed on the bridge as they would have a high tractive effort.