One way to achieve this is to set the border color transparency.
.tab-pane:focused > .tab-header-area > .headers-region > .tab:selected .focus-indicator { -fx-border-color: transparent; }
You can also set the focus color and weak focus color (used for the border of the insert).
.tab-pane:focused > .tab-header-area > .headers-region > .tab:selected .focus-indicator { -fx-focus-color: transparent; -fx-faint-focus-color: transparent; }
I used a specific class here, but it also works with the tabs class.
.tab { -fx-focus-color: transparent; -fx-faint-focus-color: transparent; }
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