I managed to add the map navigation control, remove the compass and change the zoom control background and opacity. But what about the '+' and '-' icons. How can you change the icons color, if you can?
Since the button images are set via the svg-files, they color can not be changed directly by the CSS-style. But you can specify a link to your external icons or override the fill color inside svg:
/** fill%3A%23333333 -> fill%3A%23ff0000 **/
.mapboxgl-ctrl-zoom-in {
background-image: url(data:image/svg+xml;charset=utf8,<svg%20viewBox%3D%270%200%2020%2020%27%20xmlns%3D%27http%3A%2F%2Fwww.w3.org%2F2000%2Fsvg%27>%0A%20%20<path%20style%3D%27fill%3A%23ff0000%3B%27%20d%3D%27M%2010%206%20C%209.446%206%209%206.4459904%209%207%20L%209%209%20L%207%209%20C%206.446%209%206%209.446%206%2010%20C%206%2010.554%206.446%2011%207%2011%20L%209%2011%20L%209%2013%20C%209%2013.55401%209.446%2014%2010%2014%20C%2010.554%2014%2011%2013.55401%2011%2013%20L%2011%2011%20L%2013%2011%20C%2013.554%2011%2014%2010.554%2014%2010%20C%2014%209.446%2013.554%209%2013%209%20L%2011%209%20L%2011%207%20C%2011%206.4459904%2010.554%206%2010%206%20z%27%20%2F>%0A<%2Fsvg>%0A) !important;
}
.mapboxgl-ctrl-zoom-out {
background-image: url(data:image/svg+xml;charset=utf8,<svg%20viewBox%3D%270%200%2020%2020%27%20xmlns%3D%27http%3A%2F%2Fwww.w3.org%2F2000%2Fsvg%27>%0A%20%20<path%20style%3D%27fill%3A%23ff0000%3B%27%20d%3D%27m%207%2C9%20c%20-0.554%2C0%20-1%2C0.446%20-1%2C1%200%2C0.554%200.446%2C1%201%2C1%20l%206%2C0%20c%200.554%2C0%201%2C-0.446%201%2C-1%200%2C-0.554%20-0.446%2C-1%20-1%2C-1%20z%27%20%2F>%0A<%2Fsvg>%0A) !important;
}