For a proper discussion it is probably best to separate the color bearer and different types of musicians, because they were usually made of different people and played different roles in battle.

First, musicians. A regimental musician like a drummer or bugle player was essentially a signalman. In the battlefield, bugles were most commonly associated with cavalry units. Drums were more commonly used by infantry, though a bugle would often be used as well, for reasons I'll cover later. This non usage of drums in cavalry was matter of practicality on one hand, since a drum is hard to use in the saddle, and a drum is useful for setting a marching cadence that is not needed (or useful) with horses.

We can start with drummers and fife players, though a fife would have been uncommon by the 1860s. Drummers would have been made up of young men and would not have been armed. Drums were useful for setting a marching cadence when needed for maneuvering on the battlefield prior to combat, as it improves unit cohesion and speed. Most officers pretty quickly realized that the drums were hard to hear or differentiate from the sound of gunfire when battle started. As a result, when the fighting was getting ready to start most drummers or fife players were told to retire to the rear and help medics with removing wounded soldiers on stretchers or with other necessary tasks like running messages. This was still a dangerous position to be, but they were unlikely to be targeted in particular. Civil War combat tactics usually involved a company or regiment firing at the center of an opposing company or regiment (depending on the formation), not targeting individual soldiers or personnel - sharp shooters not included, of course.

A bugler, on the other hand, was more commonly an adult soldier as it was a job of considerable importance. Some buglers were officers, and unlike a drummer, were typically armed, possibly with a saber or pistol, depending on if he was in cavalry or not, but his primary duty above all else was sending signals at the order of his commanding officer. Most companies (75-125 men) had two musicians, and almost every officer would have a signalman of some kind. A bugler, unlike a drummer, could be heard over the din of battle, and could be used to communicate orders between units. A bugler could even transmit orders from a brigade commander, which were repeated by buglers down to the regimental and company level. The commander could also send signals to his unit directly, as most people are familiar with, signaling "charge" or "retreat," and so on. Since a bugler was often at the center of a regiment or company next to the commanding officer, it was a very dangerous position to be. As a result, it was not uncommon for the officer to also know the bugle signals in case he needed to step in. A bugler, being an experienced soldier and sometimes officer, could also act independently if the moment called for it, rallying troops with signals. As I mentioned earlier, the center of the regiment was the most likely to get targeted, and Civil War officers often suffered the horrible casualty rates. For example, 27% of officers at Gettysburg became casualties, compared to 21% of general soldiers. That said, no one was targeting buglers in particular, they were just often in the most deadly place. When battle lines were formed a bugler would usually move to the back of the unit or where the commanding officer was, but did not go far, and was still in great danger.

For flag bearers, or more properly color bearers, much about buglers holds true, but its worth discussing the importance of a company's colors. The colors was a physical representation of the unit, and since many men in companies and regiments were from the same town or city, their colors were often associated with their home. It was a very real source of pride. If your company colors were captured, it was like your company had been desecrated, and your home along with it. As a result, if a color bearer was wounded, it was expected that someone else would immediately take the colors up. And if the colors risked capture, the men should rally around and defend the colors at all cost.

A color bearer was not usually armed, though he might have a sword depending on his rank. Their job was to bear the colors and stand bravely where it was easy to be seen. This was dangerous because you were at the front center of the unit. But things get more deadly from here. The company or regimental colors had to be easily seen, as it could be used as a rallying point for the unit, and was a considerable point of pride to bear the colors. If things got so chaotic that you couldn't even hear a bugle, or if they were dead along with the officers, the company colors served as a rallying point to say "we are here, and you should be here." If the color bearer fled, the unit was likely to follow them. Only the toughest and bravest men were chosen to bear the colors, because you had to stand firm in the face of anything coming at you, and know that you were a target.

Were color bearers targeted in particular? At rifle range, they probably were not, as it would have been difficult to shoot any particular person, but as I said before they are in a dangerous position. However in close combat, particularly in an assault, a color bearer would be a major target, as capturing an opposing company or regiment's colors was a major accomplishment for the attacker, and a serious blow to the pride of any unit that lost theirs. Beyond that, the colors were useful for boosting your own morale and knocking down your enemies. In an assault, when men saw the colors being raised over the ramparts or defenses of an enemy, you knew you were winning, and would bravely charge along behind them. And if you saw the enemy colors being struck down, it was a signal that that unit had been broken. A color bearer might use the staff as a weapon if things got grim, but their primary duty was to be a big colorful target.

In the British Army from at least the 18th century onwards, bandsmen would assume the role of stretcher-bearers during battle. In the absence of combat medics in the late-20th century sense, bandsmen were the closest thing the British Army in the 18th and 19th century had to medical care on the battlefield. Usually the only professional medical care which existed would be arranged on a regimental basis, with each infantry battalion or cavalry regiment having its own medical officer and possibly a small cadre of assistants. The bandsmen were the link between the front line and the medical officer. This haphazard approach continued throughout the 19th century, and the Royal Army Medical Corps (RAMC) was only formed in 1898.

Bandsmen were not armed, but not because of anything like the limitations placed on medical personnel under the Geneva Conventions and similar practices. It was simply common practice for musicians not to be issued arms on the battlefield.

During the same time period, colour parties in the British Army were formed from the regular combat personnel of a given infantry battalion. Each battalion carried two colours, a King's (or Queen's) Colour and a Regimental Colour. In Line regiments, the King's Colour was - usually - based on the Union flag with regimental numbering in Roman numerals and other features. The Regimental Colour would be based on the facing colour of the battalion, with various identifying marks and a Union flag in the upper left canton. This is slightly more complicated with the Foot Guards so I won't get into that here.

The colours - collectively called a stand - were carried by ensigns. These were the most junior officers of the battalion. Their rank is analogous to the modern rank of Second Lieutenant. These officers were usually at the beginning of their careers and would be eligible for advancement up to the rank of lieutenant colonel provided they could afford the cost of the various commissions. The colours and the ensigns were guarded by a picked group of men including senior sergeants armed with halberds or, from the late-18th century, a type of pike - called a spontoon - with a cross-bar under a large, leaf-shaped blade. They were most definitely attacked by the enemy. The British Army lost colours to the enemy on numerous occasions throughout the 18th and 19th century.