In matters other than dietary, we have to see whether there is any ethical problem present or not i.e. whether something falls in 5 broad categories mentioned in Quran (7:33) as being prohibited or not.
Principles of Determining Haram:
Discussion 1749
The same will apply here.
Twitter doesn’t generate any content on its own, but it does allow people to generate content. So what kind of content does it allow people to generate (as per their declared policy statement or mission statement etc.)? whether it allows people to generate unethical content (involving baseless allegations, nudity, blackmail etc.)?, and when someone generates this kind of content, then does it have any mechanism in place to counter that or does it allow it to happen freely? After getting answers to these kind of questions, you can decide for yourself whether such an investment should be categorized as prohibited or not.