Season 2 of Game of Thrones saw Robb Stark marry Talisa Maegyr, ultimately leading to the events known as the Red Wedding, but a change to the book meant the nuptials seemingly created a plot hole. Robb (Richard Madden) was one of Game of Thrones' early doomed heroes. The son of Eddard Stark set out to avenge his father's imprisonment and eventual execution, and it was during his warring in the Riverlands and Westerlands where he met his bride-to-be, Talisa (Oona Chaplin).
A healer on the battlefield, Talisa met Robb after he won the Battle of Oxcross. She joins his army as they move on in their campaign and, despite Catelyn Stark (Michelle Fairley)'s warnings, Robb becomes increasingly attracted to Talisa, with the pair eventually sleeping together, falling in love, and getting married (which takes place in the season 2 finale). This is partly how it plays out in the books, where Robb similarly meets a battlefield healer and ends up going through with a wedding that will cost him his life. In George R.R. Martin's A Song of Ice and Fire books, though, Robb marries a woman named Jeyne Westerling, and the difference goes beyond what the characters are called.
Robb's story with Jeyne mostly takes place "off-screen" in the books, since neither is a point-of-view character. Their relationship is often seen through the eyes of Catelyn, and readers don't get to experience their actual wedding, which itself only comes after they sleep together in order to protect her virtue, because Robb wants to do the honorable thing. That's a contrast to Game of Thrones, where the wedding is shown on screen, and is where the apparent plot hole is created. Robb and Talisa are married by a Septon, a practitioner of the Faith of the Seven, and the vows they say to one another - which reference the Seven Gods - are yet further confirmation that they are being married before the Seven. The problem a lot of fans have with this is that Robb, being of the North and Ned Stark's son, takes the Old Gods. Talisa, meanwhile, is from Volantis, and while there are various religions there, it's more likely she'd be a follower of R'hllor, the Lord of Light, or the Valyrian relgion.
Given how seriously religion and vows are typically taken in Game of Thrones - and especially are seen by the Starks, with the great Heart Tree in the Godswood at Winterfell - then it isn't something people will typically be flippant about. In the books, Jeyne is from the Westerlands, and most likely of the Faith of the Seven, so it would make more sense, but even then it's unconfirmed how the ceremony goes down. However, there are explanations for Robb and Talisa's wedding in Game of Thrones, even if the series itself doesn't go into them too much. Firstly, Robb was raised in an interfaith home - Ned takes the Old Gods, but Catelyn, as a Tully, keeps the New Gods. Winterfell had a Septa, who at least taught Arya and Sansa, and so the Stark children have grown-up around both religions. While Robb appears to take more after his father in this regard, it isn't totally out of the blue that he'd respect the Seven as well.
On top of that is also a question of circumstance. Robb & Talisa wanted to marry quickly, and weren't in the North. That means there's a real shortage of weirwood trees and anyone else who keeps to the Old Gods who could marry them. Finding a Septon and getting married in the light of the Seven was much easier to manage, especially when needing to do it in both haste and secret. This was supported by writer Bryan Cogman in an interview with Winter is Coming when asked about the matter, saying: "Shotgun wedding! Of sorts. They wanted to get married and there was a septon readily available." If given a true choice, it's likely that Robb would choose to be married before the Old Gods instead, and since Game of Thrones doesn't really explain it, it can be seen as creating a plot hole in diverging from the books, but there is nonetheless logic that can be found underpinning it.