Why do the pistols and rifles not have trigger guards? Because that is by design and not just because they do not want to animate it. Also, not all firearms in the anime do not have trigger guards.

I've yet to watch the anime but this was one of the images I found when searching for firearms in FMA:Brotherhood. In Wikipedia, real guns can have no trigger guard so

as not to impair use with large cold weather gloves on, especially those intended to be used in arctic conditions.

While this might not be in arctic conditions, the fact that some characters in the anime wear gloves proves the point that this is for ease of use. It would be difficult to press the trigger with a trigger guard if you have gloves on, especially large and thick ones.

Why do the pistols and rifles not have trigger guards? Because that is by design and not just because they do not want to animate it. Also, not all firearms in the anime do not have trigger guards.

This was one of the images I found when searching for firearms in Full Metal Alchemist: Brotherhood. A complete list of firearms from the anime can be found here, as mentioned by @Maroon, in which some standard-issue firearms have no trigger guards.

In Wikipedia, it is stated that guns can have no trigger guard so

as not to impair use with large cold weather gloves on, especially those intended to be used in arctic conditions.

While this might not be in arctic conditions, the fact that some characters in the anime wear gloves proves the point that this is for ease of use. It would be difficult to press the trigger with a trigger guard if you have gloves on, especially large and thick ones.