Can I remove the text from the tabs of the new navigation menu?

[Canapin (Coin-coin le Canapin)]

@awesomerobot

enable new user profile nav groups

You can use the following CSS:

.user-activity-page .nav-pills li span {
    display: none;
}

It doesn’t hide certain texts which aren’t wrapped in a <span> and usually come from theme components or plugins. Those can’t be targeted with CSS.