I understand that technically, yes, ending a sentence in a preposition is wrong, but should we correct people on this? In common speech, "Where are we going to?" is more accepted that "To where are we going?" How do you feel about this?
I think that if the sentence sounds completely wrong you should correct them. But if it is something that is accepted as normal and sounds fine you don't have to correct it. I mean if you want to you can, it is really just your choice.
"Where are we going?" sounds best, IMO. In speech, the rules are more relaxed. I would advise against correcting people, unless the people are your own children or students . . . it doesn't make friends (been there, done that).
Correcting someone's grammar if they have not told you they are into grammar is kind of rude. It's a silencing maneuver that's used to invalidate less educated people. Just because someone doesn't have your level of education doesn't mean their voices are less worthy. Ignoring the nature of the content of what someone says in order to privilege the quality of the form of what someone says ... is kinda snobby. If you can make sense of the sentence, it's polite not to correct. But if you are genuinely confused, it's really best to ask for clarification.
I don't correct anyone unless it's my best friend or one of my family members who, obviously, know me well. And I would advise against it anyway, especially if it's something like your example. It just makes you sound pretentious and a lot of people find it annoying.