Many of the same concepts for web pages and documents apply to social media. Also, consider the following:
Use Text With GIFs. Most social media platforms do not allow adding alt text to GIFs. Alternatively, you can add captions or text to describe the GIF.
Use Accessible Text. Screen reading technology does not do well with copy that includes emojis, special characters, or full caps. It is best to limit the use of these in your social media posts.
Use emojis appropriately. Emojis can have a negative effect on your social media posts. Avoid the overuse of emojis, and solely relying on emojis to convey meaning. The intent can become confusing and not all platforms and devices display them the same way.
Unique to Twitter
Some accessibility concerns are unique to the format.
A Twitter hashtag such as #maketwitteraccessible is a bit hard to read visually, but for a person using a screen reader, it's just gobbledygook. Add capital letters for each word and the screen reader will read each word. #MakeTwitterAccessible is easier for everyone to read. This is sometimes referred to as CamelCase (new window).
Consider placing the main content first and adding (#) hashtags and mentions at the end. This will give screen reader users the chance to evaluate if that content is of interest before wading through the links.