Can a TextView be selectable AND contain links?

I figured it out. You need to subclass LinkMovementMethod and add support for text selection. It's really unfortunate that it doesn't support it natively. I just overrode the relevant methods using the equivalent ones from the source code for ArrowKeyMovementMethod. I guess that's one benefit of Android being open source!

public class CustomMovementMethod extends LinkMovementMethod {
    @Override
    public boolean canSelectArbitrarily () {
        return true;
    }

    @Override
    public void initialize(TextView widget, Spannable text) {
        Selection.setSelection(text, text.length());
    }

    @Override
    public void onTakeFocus(TextView view, Spannable text, int dir) {
       if ((dir & (View.FOCUS_FORWARD | View.FOCUS_DOWN)) != 0) {
           if (view.getLayout() == null) {
               // This shouldn't be null, but do something sensible if it is.
               Selection.setSelection(text, text.length());
           }
       } else {
           Selection.setSelection(text, text.length());
       }
    }
}

To use it, just instantiate it directly, like so:

textView.setMovementMethod(new CustomMovementMethod());

oakes's answer cause exception on double tap on textview

java.lang.IndexOutOfBoundsException: setSpan (-1 ... -1) starts before 0...

I looked at the onTouchEvent impletentation in LinkMovementMethod and found that it removes selection when textview doesn't contain link. In this case selection starts from empty value and application crash when user try to change it.

...
if (link.length != 0) {
    if (action == MotionEvent.ACTION_UP) {
        link[0].onClick(widget);
    } else if (action == MotionEvent.ACTION_DOWN) {
        Selection.setSelection(buffer,
        buffer.getSpanStart(link[0]),
        buffer.getSpanEnd(link[0]));
    }
  return true;
} else {
  Selection.removeSelection(buffer);
}
...

So i override onTouchEvent method, and it works fine.

public class CustomMovementMethod extends LinkMovementMethod {
    @Override
    public boolean canSelectArbitrarily () {
        return true;
    }

    @Override
    public void initialize(TextView widget, Spannable text) {
        Selection.setSelection(text, text.length());
    }

    @Override
    public void onTakeFocus(TextView view, Spannable text, int dir) {
        if ((dir & (View.FOCUS_FORWARD | View.FOCUS_DOWN)) != 0) {
            if (view.getLayout() == null) {
                // This shouldn't be null, but do something sensible if it is.
                Selection.setSelection(text, text.length());
            }
        } else {
            Selection.setSelection(text, text.length());
        }
    }

    @Override
    public boolean onTouchEvent(TextView widget, Spannable buffer,
                                MotionEvent event) {
        int action = event.getAction();

        if (action == MotionEvent.ACTION_UP ||
                action == MotionEvent.ACTION_DOWN) {
            int x = (int) event.getX();
            int y = (int) event.getY();

            x -= widget.getTotalPaddingLeft();
            y -= widget.getTotalPaddingTop();

            x += widget.getScrollX();
            y += widget.getScrollY();

            Layout layout = widget.getLayout();
            int line = layout.getLineForVertical(y);
            int off = layout.getOffsetForHorizontal(line, x);

            ClickableSpan[] link = buffer.getSpans(off, off, ClickableSpan.class);

            if (link.length != 0) {
                if (action == MotionEvent.ACTION_UP) {
                    link[0].onClick(widget);
                } else if (action == MotionEvent.ACTION_DOWN) {
                    Selection.setSelection(buffer,
                            buffer.getSpanStart(link[0]),
                            buffer.getSpanEnd(link[0]));
                }
                return true;
            }
        }

        return Touch.onTouchEvent(widget, buffer, event);
    }
}

Hope it will be helpful for someone.