### Godot version

4.0.3-stable

### System information

Windows 10

### Issue description

In some projects ViewportTexture remains pink and doesn't render viewport content after upgrading from 4.0.2-stable to 4.0.3-stable. If a pair of files viewport.h/viewport.cpp are downgraded back to what they were in 4.0.2-stable, problem goes away.

This is how it looks in 4.0.3-stable:
![4 0 3_stable_viewport_4 0 3](https://github.com/godotengine/godot/assets/1449921/44c191a9-4b67-4b02-90b6-4ab615f62a73)

And this is how it looks if viewport.h/viewport.cpp are downgraded back to what they were in 4.0.2-stable.
![4 0 3_stable_viewport_4 0 2](https://github.com/godotengine/godot/assets/1449921/f5abc605-f129-4222-9c0e-e9a07621dd9d)



### Steps to reproduce

Unfortunately, I cannot come up wit a simple demo project reproducing the problem. It exists in some projects and doesn't exist in others.


### Minimal reproduction project

Cannot produce a simple project reproducing the problem. In simple projects it works fine.
ERR_MAIN_THREAD_GUARD;
	if (p_disable == disable_input) {
		return;
	}
	if (p_disable) {
		_drop_mouse_focus();
		_drop_mouse_over();
		_gui_cancel_tooltip();
	}
	disable_input = p_disable;
}
bool Viewport::is_input_disabled() const {
	ERR_READ_THREAD_GUARD_V(false);
	return disable_input;
}
Variant Viewport::gui_get_drag_data() const {
	ERR_READ_THREAD_GUARD_V(Variant());
	return gui.drag_data;
}
PackedStringArray Viewport::get_configuration_warnings() const {
	ERR_MAIN_THREAD_GUARD_V(PackedStringArray());
	PackedStringArray warnings = Node::get_configuration_warnings();
	if (size.x <= 1 || size.y <= 1) {
		warnings.push_back(RTR("The Viewport size must be greater than or equal to 2 pixels on both dimensions to render anything."));
	}
	return warnings;
}
void Viewport::gui_reset_canvas_sort_index() {