Collate a growing number of String arrays and search through them
You should use Sets instead of Arrays and Enums when it makes sense. I would write that as:

enum FeedClass {
    TEAM, DRIVER, OTHER;
    private static final Set&lt;String&gt; DRIVER_FEED_TYPES = new HashSet&lt;&gt;(Arrays.asList(
            "SEBASTIAN_VETTEL", "LEWIS_HAMILTON", "CHARLES_LECLERC", "MAX_VERSTAPPEN"));

    private static final Set&lt;String&gt; TEAM_FEED_TYPES = new HashSet&lt;&gt;(Arrays.asList(
            "FERRARI", "MERCEDES", "SAUBER", "REDBULL"
    ));

    public FeedClass fromType(String feedType) {
        if (DRIVER_FEED_TYPES.contains(feedType)) {
            return DRIVER;
        } else if (TEAM_FEED_TYPES.contains(feedType)) {
            return TEAM;
        } else {
            return OTHER;
        }
    }
}

private boolean isFeedEnabled(FormulaOneMessage formulaOneMessage) {
    FeedType feedType = FeedClass.fromType(formulaOneMessage.getFeedType());
    switch (feedType.getClazz()) {
        case DRIVER:
            return isDriverFeedEnabled();
        case TEAM:
            return isTeamFeedEnabled();
        default:
            return false;
    }
}


Driver names isn't really something that should be hardcoded, you probably want to move it to database or external file(s). 
You can't really avoid if/switch in isFeedEnabled() unless you move isDriverFeedEnabled and isTeamFeedEnabled into enum, it might not be 
 possible in your code to do it cleanly.