The appearance of Netflix subtitles can't be modified on the Netflix app or website, as one might expect. Instead they obey the local configuration of your device.
So, instead of searching the answer on Netflix, try your device's settings.
On the Settings app, go to Accessibility and then head to Subtitles & Captioning.
There you can select one of the predefined styles or you can create your own style fol subtitles. You can play around with a few options, like the color and size of text or the background.
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