This isn’t really what you’re asking for but in QGIS it’s possible to overlay arbitrary raster tile sources, like this eye-burningly awful map of iNat Quercus rubra points on top of GBIF bird hexagon bins over a Stamen Toner base layer:
The iNat and GBIF URL templates are
https://api.inaturalist.org/v1/points/{z}/{x}/{y}.png?taxon_id=49005
https://api.gbif.org/v2/map/occurrence/density/{z}/{x}/{y}@1x.png?taxonKey=212&bin=hex&hexPerTile=30&style=classic-noborder.poly
Docs:
https://www.gbif.org/developer/maps
https://api.inaturalist.org/v1/docs/#!/Observation_Tiles/get_points_zoom_x_y_png
The GBIF API supports a lot more options, and you could use it to retrieve only iNat points, too. Of course, this is only useful for visualization, not for querying.