TBH, early muskets (and the minuteman replaces the musket unit) and blunderbuss were pretty bad in terms of accuracy at range. They had no rifling grooves, fired lead balls, and had significant reload times.
A well trained archer can hit a target with great precision at or around 300-400 yards (this varies depending on the bow type (e.g. longbow,recurve, composite, crossbow, Nu, repeating Nu) and terrain) and can fire again without any special mechanism (like the repeating Nu) in under 10 seconds. If you get hit by an arrow musket ball in a critical portion of your body, your dead either way.
In point of fact, many European armies did not immediately switch to muskets from there various bowtypes because of these drawbacks, and there are many, many recorded instances of early musket armies being defeated by archery forces. This changed with the development of rifling grooves, but prior to this, non rifled fire arms were more of a close quarter combat weapon.
The second important point is terrain: If you have a group of riflemen (not musketmen mind you but actual rifled weapons) standing in an open field and a hail of arrows flies out of the forested hill 300 yards away, rifle men will die and no clear targets will present themselves in the forested hill. They can fire at the hill, but without the ability to aim and the attackers having the advantage of cover, the riflemen will get slaughtered. The clothes a riflemen or musket man wears will do nothing to prevent arrows from killing the soldiers.
When people look at conflicts for fire arms regiment versus archery regiment, they tend to look at units who have rifled weapons fighting units that have bows across an open field. But remove the rifled weapons and replace them with
smoothbore muskets and/or put the archers in concealed positions on a forested hill and you have a very different result. In point of fact, during the conflict between minutemen and redcoats, rifling had been developed, but since civ V treats minutemen as musket men, we have to overlook this discontinuity.
TL,DR: Archery with its thousands of years of honing of design and skill>early
smoothbore muskets, especially if archers have favorable terrain. This changes with rifling, but before rifling having archers beat musketmen is not unrealistic in many situations.
Edit: all of the African campaigns are poor examples of this, as IIRC the Boors and Brits had rifling, and the campaigns also featured the introduction of the Gatling.