This example requires rasterio 1.2+ and GDAL 3+.

import geopandas
import rasterio.warp
from shapely.geometry import shape

# load example data
world = geopandas.read_file(geopandas.datasets.get_path('naturalearth_lowres'))
# Reproject to Mercator (after dropping Antartica)
world = world[(world.name != "Antarctica") & (world.name != "Fr. S. Antarctic Lands")]

destination_crs = "EPSG:3395"
geometry = rasterio.warp.transform_geom(
    src_crs=world.crs,
    dst_crs=destination_crs,
    geom=world.geometry.values,
)
mercator_world = world.set_geometry(
    [shape(geom) for geom in geometry],
    crs=destination_crs,
)