Redspines are elite mooks with high health and strong attacks that possess the ability to throw javelins, which are used to soften soldiers before going in for the kill rather than as a primary attack. Redspines are otherwise fairly durable and not very easy to kill (even at later waves), and, alongside Greenfins and Deviltides, serve mostly to quickly get through towers and reduce lives while the Blacksurges and Bluegales mostly concern themselves with crippling your defenses.
Redspines supposedly have a very high physical armor rating, but this is actually not true, meaning that it's okay to use Archer Towers against them. However, make them as high-level as possible, as they have quite a lot of HP. Also, they do not appear to use their ranged attack very often, so you can stall them with whatever unit you want. However, it's recommended to use Reinforcements with the Recurve Bow upgrade rather than any other unit, as Redspines still have those spears. If you really wish to use Barracks troops against them, go for Templars or Assassins. Redspines, in addition to their toughness, deal heavy damage with each attack. With the Templars' very high HP and a 50% physical damage reduction, they can mitigate a Redspine's heavily damaging attack, whereas Assassins can conceal themselves until the Redspine is in melee range.