QGIS 3.10 also has the option of setting the symbol layer type as outline: simple line. There you have more options for setting the spacing and length of dash patterns, which can resolve some of these overlapping problems where the white solid line background doesn't help.
To achieve this while keeping fill colors of the polygons, you can duplicate the layer in the layer tree. This will not duplicate the layer file or database table, as the data source will not be altered. The duplicate can have its own settings, joins, visual representation, labels, etc.
In the duplicate layer, change the symbology (from e.g. 'simple fill') to one of the outline styles. This should give you fill polygons and no overlapping dashed lines between the polygons.