This explanation regards to all file types/snippets, the examples are
of adding react snippets.
In VSCode, snippets are loaded according to file association. You can check the current file association on the bottom bar.
Example for JavaScript React file:

Now you need to configure the snippet to the desired file type, for this you need to add files.associations property in settings.json.
File -> Preferences -> Settings -> Open Settings (JSON)
"files.associations": {
"*.react.js": "javascriptreact",
"*.stories.js": "javascriptreact",
"*.action.js": "javascriptreact",
"*.reducer.js": "javascriptreact",
"*.styles.js": "javascriptreact",
"*.jsx": "javascriptreact",
"*.js": "javascript"
}
From this point, files names like MyComponent.react.js will associate with javascriptreact type.
All is left adding your snippets to javascriptreact type:
View -> Command Palette -> Preference: Configure User Snippets
and choose a file type (if exists like javascriptreact.json or create a new file type like javascriptreactnative).
All snippets in the chosen type will associate and auto-suggests.
For example, the next snippet in javascriptreact.json will work only in React files as configured above:
"React Fragment": {
"prefix": "<>",
"body": [
"<>",
"$1",
"</>"
],
"description": "Insert React Fragment"
}
In conclusion, you need to separate .jsx extension to recognize react and react-native, for example: *.native.jsx