If your theme uses body_class() in the body tag, you will have a specific css class for the front page (.home), which you could use in the stylesheet;
Example (might be different for your theme):
.home #content .entry { color: #123edf; }
to overwerite the genral stylesheet style.css, you could use a conditional statement in header.php to link a specific stylesheet for the front page:
Example:
<?php if( is_home() ) { ?>
<link rel="stylesheet" type="text/css" media="all" href="<?php echo get_stylesheet_directory_uri(); ?>/front-style.css" />
<?php } ?>
the code needs to be after the link to the general stylesheet.
(instead of is_home() you might need to use is_front_page() )
Check: Conditional_Tags and get_stylesheet_directory_uri
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alternative, to load a different stylesheet instead of the general stylesheet, use the conditional statement with an else:
(this code would replace the link of the general stylesheet)
Example:
<?php if( is_home() ) { ?>
<link rel="stylesheet" type="text/css" media="all" href="<?php echo get_stylesheet_directory_uri(); ?>/front-style.css" />
<?php } else { ?>
<link rel="stylesheet" type="text/css" media="all" href="<?php bloginfo( 'stylesheet_url' ); ?>" />
<?php } ?>