I looked around and the most likely explanation is that you're running an ad blocker or some other content blocker which is preventing the tweets from appearing. If that's the case, try disabling the ad blocker on a page which should show an embedded tweet and see if the tweet shows up. If it does, that's your answer.

If you don't want to disable ad blocking entirely then there may be a way within your ad blocker to allow content from Twitter, which should make the tweets show up. The solution would be specific to your ad blocker though.

If you're not running an ad blocker, maybe the security settings in your browser are set to a level higher than default? Either way, it seems to be something going on in your browser that's causing this issue.