Elsa's not really sure how she's supposed to react. She's not sure how Anna wants her to react.
It would be best, she thinks, to show her support. Even if the idea makes her stomach turn a little. But it's not fair of her to drag Anna down with her own… uncomfortableness with the situation.
The best thing she can do is encourage Anna to do what makes her happy. If it's going on dates with strangers, then that's fine.
Still, Elsa mourns the loss of a friend she'd only just started understanding.