Dear sister Iman,
As I am sure you already know, believing in the existence of God is not synonymous with being a Muslim.
Most People of the book believed in God but were deemed disbeliever for disbelieving in the Quran.
[3:70]
O People of the Scripture, why do you disbelieve in the verses of Allah while you witness [to their truth]?
[3:71]
O People of the Scripture, why do you confuse the truth with falsehood and conceal the truth while you know [it]?The Mushrkeen used to believe in God but had taken up idols as intercessors.
10:18
“They serve, besides God, things that hurt them not nor profit them, and they say: "These are our intercessors with God." Say: "Do ye indeed inform God of something He knows not, in the heavens or on earth? Glory to Him! and far is He above the partners they ascribe (to Him)!"” Even the descendants of prophets were critisized and threatened for following their desires and abandoning prayer
[19:59]
But there came after them successors who neglected prayer and pursued desires; so they are going to meet evil -
Not judging by what God has revealed can amount to disbelieve. The addressees of this verse are those who have received scripture. Hence believe in God.
[5:44]
Indeed, We sent down the Torah, in which was guidance and light. The prophets who submitted [to Allah] judged by it for the Jews, as did the rabbis and scholars by that with which they were entrusted of the Scripture of Allah, and they were witnesses thereto. So do not fear the people but fear Me, and do not exchange My verses for a small price. And whoever does not judge by what Allah has revealed - then it is those who are the disbelievers.Believing in parts of the book and disbelieving in parts can lead to the most extreme of punishments. If so then what is the state of an individual who has rejected all the book. Or has taken religion in a selective manner.
[2:85]
Then, you are those [same ones who are] killing one another and evicting a party of your people from their homes, cooperating against them in sin and aggression. And if they come to you as captives, you ransom them, although their eviction was forbidden to you. So do you believe in part of the Scripture and disbelieve in part? Then what is the recompense for those who do that among you except disgrace in worldly life; and on the Day of Resurrection they will be sent back to the severest of punishment. And Allah is not unaware of what you do.Therefore, in my humble opinion being decent and of a good family is one thing. But believing and accepting islam is quite another. If she accepts the whole "islamic package" willingly not out any external pressure then I believe then, it would be acceptable.
And let us remember the verse Brother Duster shared:
[2:221]
And do not marry polytheistic women until they believe. And a believing slave woman is better than a polytheist, even though she might please you. And do not marry polytheistic men [to your women] until they believe. And a believing slave is better than a polytheist, even though he might please you. Those invite [you] to the Fire, but Allah invites to Paradise and to forgiveness, by His permission. And He makes clear His verses to the people that perhaps they may remember.So yes I share your concern and I believe it is a valid one indeed.
Hope this helps in a small way
Regards,
Ahmad.
References:
[1] Idolatry according to the Quran
http://quransmessage.com/articles/idolatry%20according%20to%20the%20quran%20FM3.htm