It's playable, I don't see any problem.
Kingside castling against the London
black doesn't really take on e5 without a follow-up in the d5 lines vs the london. here it just gives up the bishop pair for nothing. maybe even stronger is dxe5 going for an attack.
also in this line you gave black did not attempt to play c5 or try to exchange light squared bishops with ba6 or try to install a knight on e4. usually he will be able to do one of these and prevent you from attacking so easily. you should study how white plays when this happens.
I use to play at club level but stopped playing for the last 20 years, so i am very rusty. I always used to play e4 at the time, but currently i am playing daily chess at around 1400-1500 and i've decided that to get back into it when White I will play the London. What i am finding is that most opponents castle early on the kingside against my London. Maybe it's the level we at, but i think it's a bad mistake, because it allows me to attack the king side with the pawns and bishops, while my king is tucked safely on the second row in the middle. Here is an example of an early phase.
What do you think, is it a mistake?