Verse 5:5 permits marriage with people who have been " given the book before you ":
Quran 5:5 ... And [lawful in marriage are] chaste women from
among the believers and chaste women from among those who were given
the Scripture before you ...
And it is understood by the majority of the scholars that it includes Christians, trinitatians or otherwise. This is because the Christians had similar beliefs in the time of the Prophet (p.b.u.h) and the Quran itself mentioned that Christians consider Jesus to be divine [5:72], and that they believe in trinity [5:73] and knowing that, it did not specifically exclude them in 5:5.
A group has opposed the above, because of the following verse:
Quran 2:221 And do not marry mushrikati (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 mushrikeena ( 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.
And cited the view of Ibn Umar:
Saheeh Bukhari Whenever Ibn `Umar was asked about marrying a
Christian lady or a Jewess, he would say: "Allah has made it unlawful
for the believers to marry ladies who ascribe partners in worship to
Allah, and I do not know of a greater thing, as regards to ascribing
partners in worship, etc. to Allah, than that a lady should say that
Jesus is her Lord although he is just one of Allah's slaves."
The majority, however, argues that 2:221 is about polytheist idolators and does not extend to Christians, since the Quran normally uses mushriqeen to only refer to the idolaters and the Christians are usually separately mentioned as Nasara (meaning Christians) or as Ahle Kitab (people of the book) ... for example consider:
إِنَّ الَّذِينَ آمَنُوا وَالَّذِينَ هَادُوا وَالصَّابِئِينَ
وَالنَّصَارَىٰ وَالْمَجُوسَ وَالَّذِينَ أَشْرَكُوا إِنَّ
اللَّهَ يَفْصِلُ بَيْنَهُمْ يَوْمَ الْقِيَامَةِ ۚ إِنَّ اللَّهَ عَلَىٰ
كُلِّ شَيْءٍ شَهِيدٌ
Indeed, those who have believed and those who were Jews and the
Sabeans and the Christians and the Magians and
those who associated with Allah - Allah will judge between them on the Day of Resurrection. Indeed Allah is, over all things, Witness.
مَّا يَوَدُّ الَّذِينَ كَفَرُوا مِنْ أَهْلِ الْكِتَابِ وَلَا
الْمُشْرِكِينَ أَن يُنَزَّلَ عَلَيْكُم مِّنْ خَيْرٍ مِّن
رَّبِّكُمْ ۗ وَاللَّهُ يَخْتَصُّ بِرَحْمَتِهِ مَن يَشَاءُ ۚ وَاللَّهُ
ذُو الْفَضْلِ الْعَظِيمِ
Neither those who disbelieve from the People of the Scripture nor
the polytheists wish that any good should be sent down to you from
your Lord. But Allah selects for His mercy whom He wills, and Allah is
the possessor of great bounty.
لَمْ يَكُنِ الَّذِينَ كَفَرُوا مِنْ أَهْلِ الْكِتَابِ
وَالْمُشْرِكِينَ مُنفَكِّينَ حَتَّىٰ تَأْتِيَهُمُ الْبَيِّنَةُ
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 -
Another group holds that if 2:221 included the People of the Book then 5:5 abrogated it in their regard, since Maidah was revealed after Baqarah.
There is a detailed discussion of this and the arguments and counter-arguments in:
Tafsir Al Jassas on 2:221 and 5:5
Tafsir Al Qurtubi on 2:221 and 5:5
I'll add in my personal opinion (against the majority view): I believe that Christians shouldn't be included in 5:5 and should be excluded because of the spirit (if not the literal meaning) of 2:221, and that 5:5 should only be limited to practicing Jews and those among the Christians who are Unitarian and observe the laws of the Torah.