Is it best to keep twins together in the same class?

I think the decision depends on how they get along. If they like working as a team and enjoy being together, same class might work great. As they are growing older it can be discussed with them (obviously in an age appropriate way).
Another important factor is if they are identical twins or fraternal. Identical twins do struggle with developing their individual identities because people fail to recognize or differential them. Exceptions are still there, I had twin sisters in my class (in senior school), and they loved getting all the attention from class mates and teachers.
As for fraternal twins, they are just like siblings who were born together. The look different and have different personalities.
Parents can keenly observe their twins, discuss it with them and their teachers to arrive at a good decision.

I think it can go either way... There are a few variables to keep in mind as every pair of twins are so different. As previously stated, if the twins get along in their classes together then there would be no concern at this stage to separate. If however, one twin is more favoured or compared to their sibling, it might become an uncomfortable situation where one twin may become discouraged. If they are competitive or distracted by each other, this might be another reason over time to separate for individuality. Also, if they tend to be dependent on each other and don't socialise well with others, this might make their social-emotional experience more difficult as well. Its always most helpful to hear the childrens' points of view as well as take into consideration your own or the teacher's observations before making the decision to separate.

As a teacher, my opinion on this is that it depends on the twins. Yes, some twins benefit from being separated but others don't. Connection is so important and if your twins have been together with no issues then i don't see any reason to separate them now. I think definitely talk to them about it and ask them what they would like to do and have a chat with the teachers. It sounds like you have a very healthy attitude towards supporting your twins at school.

I don't have twins, but I have a lot of friends with twins and they have wondered the same thing. I think it can go either way. I think now that they are a little older, you can talk to them about what they might want. I've seen success in both scenarios. They might have a very strong opinion about sharing a class with their twin. If they stay in the same class, they can always do separate after school activities. But I think in second grade they are old enough to express their opinion on what they want to do.

Even if they aren't in the same class, they will have a lot of opportunities to see each other in school and have their shared group of friends play together. You might run into "but he/she got the better teacher!" and things like that...just a heads up! I think as they get older, they're going to naturally go their separate ways (especially in the school environment) and it's up to you as a family how quickly you want that to happen.