Как переопределить базовый класс дочерним шаблоном?

Вы можете попробовать что-то вроде следующего.

#include <string>
#include <map>
#include <utility>
#include <vector>
#include <cmath>

class Configuration
{
protected:
    static std::map<std::string, Configuration *> commands;
    static std::vector<Configuration *> commidx;

    const std::string name;
    const int index;
    int (*snippet)(float);

public:
    Configuration(std::string name, const int index, int (*snippet)(float))
        : name(std::move(name)), index(index), snippet(snippet) {}
    virtual ~Configuration() = default;
};

template <typename T>
class ConfigurationBase : public Configuration
{

public:
    ConfigurationBase(std::string name, const int index, int (*snippet)(float))
        : Configuration(name, index, snippet)
    {
    }
    //virtual void set(T val) {}
    //virtual T get() { return NAN; }

    virtual void set(T val) = 0;
    virtual T get() = 0;
};

template <typename T>
class Config : public ConfigurationBase<T>
{
    const std::string type;
    const std::string def;
    T cur, min, max;

public:
    explicit Config(const char *name, int index, const char *_type, const char *def, int (*snippet)(float), T min, T max)
        : ConfigurationBase<T>(name, index, snippet), type(_type), def(def), min(min), max(max)
    {
        if (type == "float")
        {
            cur = std::stof(def);
        }
        else if (type == "integer")
        {
            cur = std::stoi(def);
        }
        else if (type == "bool")
        {
            cur = std::stof(def) != 0;
        }
        else
        {
            // SPDLOG_ERROR("unknownt type {}", type);
        }
    }

    void set(T val) override
    {
        if (val < min)
            val = min;
        if (val > max)
            val = max;
        if (val != cur)
        {
            val = cur;
            // snippet(val);
        }
    }

    T get() override
    {
        return cur;
    }
};

std::vector<Configuration *> Configuration::commidx{
    new Config<float>("fff", 0, "float", "0.4", nullptr, 0, 1),
    new Config<bool>("bbb", 1, "bool", "0", nullptr, 0, 1),
    new Config<int>("iii", 8, "int", "0", nullptr, 0, 3),
};