In a block you can switch off caching of the rendered View in ViewExecutable::buildRenderable:
$view->buildRenderable('views_block_id', $args, FALSE)
because the rendered result of each block instance is already cached.
By the way, cache tags are not involved when caching variants of the same element. This is only controlled by cache keys and contexts. ...
This is a problem I've encountered numerous times, and personally I've never had any luck outputting inline styles in a Views field that's been rewritten through the UI.
My solution has always been to create a template file that takes responsibility for rendering the view fields, as that does allow you to use inline styles.
In your case, you could have the ...