Twitter recently blocked Instagram from fetching user contacts to let them connect with their friends on the Instagram platform.
Instagram has responded by disabling support for Twitter Cards.
This means that Instagram shares on Twitter would no longer appear as rich embeds. Users might see a cropped photo at times but mostly, the links from Instagram would appear as just links.
This applies to official Twitter clients on desktop and mobile platforms. It does seem to work on their web app right now though.
Users are experiencing issues with viewing Instagram photos on Twitter. Issues include cropped images. This is due to Instagram disabling its Twitter cards integration, and as a result, photos are being displayed using a pre-cards experience. So, when users click on Tweets with an Instagram link, photos appear cropped.