You can add any Mapbox map as a layer in ArcMap or QGIS as WMTS.
At the top of the dialog box, click the arrow next to Look in: and select GIS Servers.
Double-click Add WMTS Server to open the Add WMTS Server dialog box.
In the Server Layers section, click Get Layers. When prompted for a username and password, click Cancel. You may have to click it several times to dismiss the box.
When the layers are loaded in the window, click OK.
You should see Mapbox on api.mapbox.com in the Add Data dialog box. Double click it, select the name of your style in the next dialog box, then click Add.
You should see your map as a layer inside your ArcMap document. Note that each style will have to be added individually.
In QGIS, click the Add WMS/WMTS button.
Give the layer a name and add the URL for your style’s WMTS endpoint. This can be found on the style’s share page. Press OK.
Back in the Add Layer(s) from a WM(T)S Server dialog box, the name of your layer should appear in the box at the top. When you see this, click Connect.
The Tilesets tab should open with a single layer. Select that layer and click Add, then click Close to close the dialog box.
You should see your map as a layer inside your QGIS document. Note that each style will have to be added manually.