GOD the Father
This one is easy. The Father is an authoritarian figure; indeed He produced the Ten Commandments as a definite policy. He must be a Conservative, probably even a Thatcherite. He would certainly be described as "Strong and Stable".
Allowing the vast majority of his people, except for a wealthy yacht-owner (Noah) and his family, to be drowned in a flood, is the sort of policy that conservatives can only look on with envy.
All right, there's some stuff in the psalms about the Lord being a shepherd, and people lying down in green pastures (definitely appealing to the Greens), but generally the Old Testament has little to say about carbon footprints and recycling plastic bags. So a Tory He must be.
"Vote Conservative! Mind you, I'm not all that keen on Theresa May."
GOD the Son
Jesus is easier to pin down, as He is the only one of the Trinity who is actually human. He was very keen on helping the poor, so it is not surprising that the Labour party would like to claim Him. After all, their main appeal is to poor people such as celebrities (footballers, actors, BBC comedians, etc.), doctors, professors, etc. Oh and a few ex-miners and ex-steelworkers aged about 95.
The other reason why we assign Jesus to the Labour party is that He bears a distinct resemblance to the young Jeremy Corbyn, although without his fondness for Marxism, terrorism, etc. Indeed, as a Jew, Our Lord might feel unwelcome in the modern Labour party.
The IRA theatre players with their re-enactment of the Last Supper.
Still, the "what would Jesus do" people tend to focus on His "Labour" credentials as a touchy-feely softie, rather than His habit of chastising people with ropes of knotted cord (surely a UKIP habit?) - not to mention the threats of Hellfire - so let's provisionally assign Him to Labour.
GOD the Holy Spirit
The problem with the Holy Spirit is that He (or She if you believe James Martin SJ) has never been known to make a precise statement. A lot of hot air rushing around with good intentions... well, that suggests the Liberal Democrats.
"Kumbayah, Lord," say the Lib Dems.
You'll find that the people who mention the Holy Spirit a lot (especially when implying that Christ's teaching could do with a little updating) would fit in well with the Lib Dems: think of their leader Tim Farron and his "these are my principles, but if you don't like them I've got others" attitude to abortion and same-sex weddings.
So, according to the Trinity, we must expect a hung parliament. Of course, by looking at the early church, we can find representatives of other parties: St Andrew, the Scottish disciple, would be SNP; St Peter, with his suspicion of foreigners, would be UKIP, and so on.
Maybe we can get more guidance by asking a bowl of porridge.