I'm sure I've kindled quite a debate going by the title. But let's not deny the fact that at least one of the partners is bound to experience this. While I have my own reservations about it, I went around asking people what they feel about being in this situation and by the responses I got, I could broadly classify it as:
1. It is absolutely okay to develop feelings for someone else while being in a relationship:
So, having a crush on someone while you're already dating is completely fine according to some. And this is because emotions, feelings, infatuation all of this comes naturally to us. I mean, we can't possibly control our fondness for someone, it just happens. Let's say we befriend that person and get to know them and you realize he/she doesn't even come close to your partner, I'm sure it will make you respect your s.o. even more. And should we be even making a big deal of this? Probably no.
2. This could bring in a lot of trouble for you, to begin with:
Now, while on the plus side you would not be actually developing feelings for someone else and they turn out to be a d-bag, what if it gets real? What if you get to know the person and you actually start liking them. This will be challenging for you first and will eventually affect your relationship. It becomes tougher for you because the only person who can help you is yourself. You can't confess your feelings for the other person and no way in hell can you tell your partner about your situation initially. An interesting perspective on this is if you're falling for someone else, you never really were in love with your partner.
In my opinion, this experience is subjective. While you can be completely okay with liking someone else while being in a relationship (some couples are also open to this) for some this may be a huge problem. In either situation, communicating with your partner becomes a must. In this way, you both remain on the same page.