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The following compiles:

Or, to avoid the use of typedef, you can use the following:

For one thing, you are using the variable state without defining it. Moreover, you have not declared the functions CheckEntrySensor() and throwRelayAndCheckStatus() . When you define a function without first declaring it, the arduino preprocessor builds its own declarations, but often does so in a defective way. This is one of the idiosyncracies of the arduino environment versus a plain C++ compiler.

The following compiles:

Or, if you want to avoid the use of typedef, you can use the following:

Or, to avoid the use of typedef, you can use the following:

enum RelayState { RELAY_OFF = HIGH, RELAY_ON = LOW };
enum CrossingZoneState: uint8_t {
    CROSSINGZONE_CLEAR = 0, // no train in crossing area, also initialized state
    CROSSINGZONE_OCCUPIED = 1, // train detected by the entry sensor
    CROSSINGZONE_EXITING = 2  // train detected by the exit sensor, when sensor clears, state= Clear
};

enum CrossingZoneState CheckEntrySensor(uint8_t esp) ;
boolean throwRelayAndCheckStatus(uint8_t relayNumber, enum RelayState relayState) ;


enum CrossingZoneState CheckEntrySensor(uint8_t esp) {
    enum CrossingZoneState state ;
    //esp, short for entry sensor pin
    if (digitalRead(esp) == HIGH)
    {
        state = CROSSINGZONE_CLEAR;
        return state;
    }
    else if (digitalRead(esp) == LOW)
    {
        state = CROSSINGZONE_OCCUPIED;
        return state;
    }
    // if the digital read errs, return the current state so it re-runs
    return state;
}

boolean throwRelayAndCheckStatus(uint8_t relayNumber, enum RelayState relayState)    {

    int testInt = 0;
    if (relayState == RELAY_OFF)
    {
        testInt = 1;
    }
    digitalWrite(relayNumber, relayState);
    if (digitalRead(relayNumber) == testInt) {
        return true;
    };
    return false;
}

The following compiles:

enum RelayState { RELAY_OFF = HIGH, RELAY_ON = LOW };
typedef enum RelayState RelayState_t ;


enum CrossingZoneState {
    CROSSINGZONE_CLEAR = 0, // no train in crossing area, also initialized state
    CROSSINGZONE_OCCUPIED = 1, // train detected by the entry sensor
    CROSSINGZONE_EXITING = 2  // train detected by the exit sensor, when sensor clears, state= Clear
};
typedef enum CrossingZoneState CrossingZoneState_t ;

CrossingZoneState_t CheckEntrySensor(uint8_t esp) ;
boolean throwRelayAndCheckStatus(uint8_t relayNumber, RelayState_t relayState) ;

CrossingZoneState_t CheckEntrySensor(uint8_t esp)
{
  CrossingZoneState_t state ;
    //esp, short for entry sensor pin
    if (digitalRead(esp) == HIGH)
    {
        state = /*CrossingZoneState_t::*/CROSSINGZONE_CLEAR;
        return state;
    }
    else if (digitalRead(esp) == LOW)
    {
        state = /*CrossingZoneState::*/CROSSINGZONE_OCCUPIED;
        return state;
    }
    // if the digital read errs, return the current state so it re-runs
    return state;
};

boolean throwRelayAndCheckStatus(uint8_t relayNumber, RelayState_t relayState)    {

    int testInt = 0;
    if (relayState == /*RelayState::*/RELAY_OFF)
    {
        testInt = 1;
    }
    digitalWrite(relayNumber, relayState);
    if (digitalRead(relayNumber) == testInt) {
        return true;
    };
    return false;
};

The following compiles:

enum RelayState { RELAY_OFF = HIGH, RELAY_ON = LOW };
typedef enum RelayState RelayState_t ;


enum CrossingZoneState {
    CROSSINGZONE_CLEAR = 0, // no train in crossing area, also initialized state
    CROSSINGZONE_OCCUPIED = 1, // train detected by the entry sensor
    CROSSINGZONE_EXITING = 2  // train detected by the exit sensor, when sensor clears, state= Clear
};
typedef enum CrossingZoneState CrossingZoneState_t ;

CrossingZoneState_t CheckEntrySensor(uint8_t esp) ;
boolean throwRelayAndCheckStatus(uint8_t relayNumber, RelayState_t relayState) ;

CrossingZoneState_t CheckEntrySensor(uint8_t esp)
{
  CrossingZoneState_t state ;
    //esp, short for entry sensor pin
    if (digitalRead(esp) == HIGH)
    {
        state = /*CrossingZoneState_t::*/CROSSINGZONE_CLEAR;
        return state;
    }
    else if (digitalRead(esp) == LOW)
    {
        state = /*CrossingZoneState::*/CROSSINGZONE_OCCUPIED;
        return state;
    }
    // if the digital read errs, return the current state so it re-runs
    return state;
}

boolean throwRelayAndCheckStatus(uint8_t relayNumber, RelayState_t relayState)    {

    int testInt = 0;
    if (relayState == /*RelayState::*/RELAY_OFF)
    {
        testInt = 1;
    }
    digitalWrite(relayNumber, relayState);
    if (digitalRead(relayNumber) == testInt) {
        return true;
    };
    return false;
}