I do think if someone is having an 'alternative' Christmas Day meal, they should say what they're planning, before inviting guests who can then either accept or politely decline the invite.
Most people would probably expect a traditional turkey with all the trimmings, and may be disappointed with an Indian takeaway, which they could have any day of the week.
Saying that, if we were invited to DS, or DDs for Christmas Day, and they weren't cooking turkey, I'd be happy with anything they offered. However, we always do the full turkey & trimmings, and I know that they'd be the first to complain if I decided to offer them an alternative!