Asalamu 3alykum
I think its important to read the Quran from the view of those who are the first recipients of it.
The first recipients are prophet Muhammad(pbuh) and his people. Its clear from many verses that the prophet and his people are uneducated about the Abrahamic faith. They are termed to be "ummiyoun". They are called to faith and there are some who believed(Aamanu) and there are some who rejected(kafaru). God repeatedly calls them and separates them from different people in their surroundings. This does not mean they are the only believers(muslims).
Its also clear that in the prophets vicinity there are others who are from the Abrahamic faith who speak Arabic. They are termed to be People of the Book, Bani Israel, Yahuud, Nasara, etc.
The term "Muslim" as a label for a nation as a whole does not to seem to be established in that time like in todays world.
Anyone of those who received guidance from God and follows it is a Muslim from a Quran's perspective. The Christians, and the Jews would of had a equivalent word that means Muslim in their own language.
Verse 5:5 is making it clear to a new community that those chaste women who also come to belief and those who are chaste from the people of the book are lawful in marriage to them.
The reason God has put the believing women in a separate category is to make it clear that those who are also muslims from the people of the book are also lawful in marriage. Its also to make it clear that not only the people who believe in the Quran are Muslims but also those who are from the people of the book. In this verse the context is clear, that the people of the book who are being mentioned are the ones following the truth and not the ones who have taken a wrong path as for example worshipping other Gods or ascribing partners to God. One can tell what path is wrong or right by collaborating their ways with the message of the Quran. All the Scriptures must be consistent.
You said
also when Allah spoke in this verse he didn't specify which group of christians are eligible for marriage..He spoke in general ie people of the book ..He did not say "believing people of the book"
There is no reason to say "believing people of the book" as the context is key and tells which ones God is speaking of. Its also clear from the Quran that:
3:113 Not all of them are alike: Of the People of the Book are a portion that stand (For the right): They rehearse the Signs of Allah all night long, and they prostrate themselves in adoration.u said : Not those who were given the Book but are seen as polytheists .... why do u say they are polythiest? sura elbayena aya 1 definitely excludes them from polythiesm " Those who disbelieved among the People of the Scripture and the polytheists were not to be parted [from misbelief] until there came to them clear evidence "
What I meant by polytheists are those who worship more than one God. Like some Christians who take Jesus as a lord or a son of God I would say they are not monotheists but polytheists. Either way I should of explained it different.
The verse you mentioned is capturing a people who have rejected(kafaru) the Quran in the prophets time. The verse is clear that those who have rejected the Quran from those who received a Scripture from God(Jews,Christians) and those who are polytheists(mushrikeen)(from the ummiyoun,) are not going to be parted from their decision of rejecting the Quran until clear evidence comes to them.
Here God is telling us about people of the scripture regardless of whether they are ascribing partners to God or not they are at least rejecting the Quran and God is also telling us about another group of people who were presently mushrikeen(ascribing partners to God) who also rejected the Quran.
Again the reason the Quran separates the polytheists from the people of the book is because thats exactly how people perceived themselves and its because thats how they were.
You said
i think we can eat or marry form christians in general and the distinction between christians that u refer to is related to Allah's relation to them not ours...because like i said when Allah allowed us to marry and eat their food He did not mention 'which" christians He spoke of them in general.
I would have to respectfully disagree with that statement.
The food that is spoken of in that verse is about the lawful food prescribed to them in truth and the marriage from the People of the Book is not from those who ascribe partners to God as it would go against the spirit of the Quran and this verse
2:221 Do not marry idolater women unless they believe in God. A believing slave girl is better than an idolater, even though the idolaters may attract you. Do not marry idolater men unless they believe in God. A believing slave is better than an idolater, even though the idolater may attract you. The pagans invite you to the fire, but God invites you to Paradise and forgiveness through His will. God shows His evidence to people so that they may take heed.
You said
another point is that Allah has put both the christians and jews in one group ie people of the book even thu the jews do not belive in the trinity.. so being "of the book " is stauts given to those with the devine book regardless of the trinity issue.
I think its more to it than just the trinity issue. I would say in my personal humble opinion that its about faith. The message seems to be encouraging the recipients of the Quran to marry believing practicing women from the people of the book who also recognize the Quran as the true faith. This is more than hinted in verse 5:5 as it allows for the People of the Book to lift the restrictions of food that was once forbidden for them and with the acceptance of the Quran, verse 5:5 becomes in effect and they may now eat from all the food the Quran has made lawful.That being said they would by default accept the Quran testimony. They are not asked to convert but that they understand or accept the Quran is also the word of God.
I would also have to safely say the verse does not restrict men from marrying women from the people of the book who follow their guidance in truth(making sure they are not amongst those who ascribe partners with God) regardless if they believe in the Quran or not.
Salam