Does anyone know if there are any applications can support exporting Shapefile to GeoJSON and keeping the style?
GeoJSONs do not store style, just feature geometry and attribute data. The only way you could save the style is if you were to embed the style properties as an attribute, for instance creating an attribute called
colour and populating it with what colour each feature should be.
Incidently, shapefiles do not store style, either. The style is applied by whatever application is loading the data.