On clicking on any social media link, say Twitter, it opens on same tab.
So I think it would be better if it opens in a new tab.
I mean the link is available here.
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Nothing should open in a new tab automatically. A user who wants to do that has the ability to do so; you shouldn't take the choice away from those who don't want this behavior.
A few things on SE (Community Bulletin links are the example I remember) used to open in a new tab. That raised the question of why those links and not others? The inconsistency confused people and, as I noted, there was no good reason for it. I believe the only SE links that open in new tabs now are ads, and treating ads this way is common enough on the web that people probably aren't surprised by it.
If you want to say the difference is on-site versus off-site links (SE question uses the same tab, social-media link uses a new tab), then you still have a problem -- why the social-media links in the profile but not external links in the "about" text or in post bodies?
The principle of least astonishment calls for not doing this and especially not doing it inconsistently. The vast majority of the web opens links in the current tab; it's why browsers have a right-click option (or control-click or long-tap) to do otherwise. It's what people expect. Don't mess with that.