This is quite a good question. There is no simple solution for it.
Nowadays prime meridian is still in Greenwich but it was slightly moved from the original 0° 0' 0'' position (shifted by 5.34 arcseconds). It is denoted as IERS Reference Meridian (IRM). The prime Meridian should be on a plane, which splits the Earth's mass into exact halves. Due to higher resolved data on the Earth's shape and mass distribution, one realized that this was not the case for the 'original' prime Meridian. See Malys et al. (2015) [doi: 10.1007/s00190-015-0844-y] for details.
Movement of Tectonic Plates
As you say: the continental plates move. Thus, a global perfect map from 1985 would differ from a global perfect map from 2017. If we keep our lon-lat-coordinate system constant, some real world locations move with respect to their geographical coordinates.
At this point a 'reference datum' comes into play: one fixes the coordinate system on a specific date and for a specific tectonic plate. Examples are the North American Datum 1983 (NAD83) and the European Terrestrial Reference Frame 1989 (ETRF89). Thus, using NAD83, a specific building in New York did not 'move' between 1985 and 2017. With respect to ETRF89 it would have moved.
Further problems: shape of the Earth
We need to assume a defined shape of the Earth to map coordinates to geographic places. The simplest assumption is: the Earth is a perfect sphere. However, this is not the case. GPS coordinates are based on the World Geodetic System of 1984 (WGS84). It uses a ellipsoid is shape for the Earth and the IRM as reference meridian. The English Wikipedia article is quite detailed.
If we assume another shape for the Earth but the same zero-meridian, most geographic locations will be projected on slightly different coordinates than they currently have. In order to maintain consistency of lon-lat-coordinates, standards like WGS84 and data like NAD83 were defined on an international level.