My mother is Jewish but my father is Christian and I was raised in the Christian church, but I still have a lot of respect for my Jewish heritage. Would it be wrong to wear a Star of David necklace, or would that offend people?
Thank you for your sensitivity in asking this question.
As pointed out in comments, you are actually Jewish (whether you follow Judaism or not). But as you say in your question, you've been raised with Christianity and it doesn't appear that you've rejected that. You see Judaism as part of your cultural background, if I'm reading you correctly, the way Christians see some events in the Hebrew Bible as historically important but not personally, religiously relevant. (That is, things like the lives of the patriarchs, the slavery in and exodus from Egypt, the 40 years in the wilderness, and most especially the laws given by God are not generally seen as part of one's core and personally binding; they are part of the background of Judaism from which Christianity formed.)
You should therefore consider the context in which you wear the necklace. In your day-to-day life, are you mainly in secular settings and religion doesn't tend to come up? Sure, I doubt anybody's going to object to that. Be prepared for the occasional person to ask you if you're Jewish. Inoffensive answers there would include "my family is" or "it's part of my background" or "not really, but I like the necklace". While saying "yes" is halachically correct (you are, because your mother is), I would advise against saying that in a setting where people would interpret that as a statement of belief. If you don't follow the Jewish religion, you may confuse people.
I would advise against wearing it in an overly-religious setting, such as when attending church. That's bound to confuse some people, and since some Christian denominations are supersessionist, claiming that their religion replaces God's covenant at Sinai, you could be inadvertantly making a theo-political statement. If you don't mean to it's confusing; if you do mean to, to Jews who know about it, it's somewhat offensive. See also this related question about a necklace containing both a star of David and a cross; some of those issues could apply when wearing a (plain) star of David in a Christian setting.
That must sound like a complicated and long-winded answer to what you may have thought was a simple question. Sorry about that. My bottom-line advice is: consider the message your wearing it might send in the place where you're wearing it, and then decide whether to wear it at that time. I don't want to discourage you from being proud of your Jewish heritage, and I hope that you'll decide to learn more about it over time.
(I don't have any sources. This advice is based on many interactions, and some longer-term relationships, with both interfaith families and converts in training. Figuring out the "identity" part of Judaism, and symbols that convey this identity, can be pretty confusing sometimes.)
The only thing that would be offensive is if you posed as accepting the Jewish faith and then went around telling everyone that they have to believe in Jesus.