So, these kids wake up in Grimgar with no knowledge of who they are, other than a name. Some of them are even forming romantic couplings. What guarantee do they, or the audience, have that they're not related where they came from originally?
Characters appear to have a vague sense of déjà vu when they run into someone they knew from their previous life. If the feelings were strong, such as hate or love, those emotions still linger: though the characters don't understand why they're having those feelings. If any of the characters were blood related, they'd feel that family relationship between each other, though they could not explain the source. This would prevent an incestuous encounter, unless said characters were already emotionally inclined that way.
The light novel later reveals that Grimgar is connected to other worlds, of which Earth is only one of many. In the very first chapter, the characters decide to follow Renji through a darkened passage, which leads to Grimgar. During this scene, Kikkawa mentions the tunnel also went another direction, but Renji dismissed him and kept walking towards the Grimgar direction. When they exit the passage, it promptly seals behind them, and everyone forgets the passage ever existed. It's possible going the OTHER direction that Kikkawa suggested, would have taken them back to Earth.
It's also possible going the other way could have taken them to a world WORSE than Grimgar.
The characters that died in Haruhiro's party weren't part of the original group that left Britney's shop. Manato joined and took leadership several hours later, after gathering information. Moguzo joined over a week later. Mary joined as the replacement priest for Manato several months down the road. Also their names all start with the letter M.