Most performant design for each member to manage his/her own news list? Say a news website has news categories such as Politics, Business, Society, Education, Health, Tech, Celebrity, Lifestyle, ... etc. The number of categories may be more than 20. New categories may be added; existing categories may be deleted.

If a registered member has no desire to see the news of a certain categories, he/she should be able to block those news so that those news don't show up in the news list on the homepage. This will only affect himself/herself, of course. Other members have their own preferences.

Each member can visit the Manage News Categories page to block/unblock news categories. The page will contain a HTML &lt;form&gt; with &lt;input type="checkbox"&gt;s of news categories.

What's the most performant database design for such a feature?

I'm currently not an expert of database design. My initial thought is creating an associative table called "member_category_map" and associate it with the "members" table and the "categories" table.

Not sure if I'm being naive, but I'm worrying that the "member_category_map" table might end up containing too much data. Assuming that there are 20 categories and each member only blocks 1 category. If there are 2,000,000 members, then the "member_category_map" would contain 2,000,000 * 19 = 38,000,000 data. I don't know if that's good for performance.

Advices are much appreciated. Thanks.
You need four tables:  

User            Category           Article                  Pivot
+----+-----     +----+-------+     +----+--------+-----     +---------+--------+
| id | ...      | id | title |     | id | cat_id | ...      | user_id | cat_id |
+----+-----     +----+-------+     +----+--------+-----     +---------+--------+


Table Pivot is standing for M:N relation and contains the subscription pairs user:category. Each user can have 0..n categories subscribed and each category can be subscribed by 0..m users. To fetch articles accordingly to the user's subscriptions you need to use JOINs like that:

SELECT u.name  AS UserName
     , c.title AS Category
     , a.id    AS ArticleID
     , a.title AS ArticleTitle
     , a.date  AS ArticleDate
     , a.url   AS ArticleLink
     -- everything you need 
  FROM user      AS u
  JOIN pivot     AS p  ON p.user_id = u.id     -- pivot to user first
  JOIN articles  AS a  ON a.cat_id = p.cat_id  -- articles and
  JOIN category  AS c  ON c.id = p.cat_id      -- categories to pivot then
 WHERE u.id = 12345
 ORDER BY a.date DESC
 LIMIT 10
;


For the best performance you need to index tables by the columns used by the query:
user should have the primary Key (id)
article should have the multicolumn key (id, cat_id, date)
pivot should have the multicolumn primary key (user_id, cat_id) with FKeys to the corresponding tables.