I don't really classify this one as a typical harem anime. In a typical harem, the guy in question is either totally bland or else a notably pathetic loser.
The hero of this series is a little above average in his decency, bravery and decisiveness. I tend to think that girls would give him a chance even in his own world.
However, he's gotten to a world, showed his mettle, won some battles, and reaped some rewards. This guy is a winner. Girls like winners. The fact that girls keep hitting on him is not unrealistic.
I really like the main female character as well. Given her aristocratic upbringing, her family pressures, and her peer pressures, her personality is absolutely convincing to me.