C++, 195 bytes

Uppercase, return true if input is a strong word, false otherwise ( C++ have simple int to bool implicit cast rules, 0 => false, true otherwise )

#include<string>
#define C(p)(v.find(e[p])==size_t(-1))
std::string v="AEIOUY";int s(std::string e){for(int i=0;i<e.size()-1;++i)if(e[i]>64&&e[i]<91&&C(i)&&C(i+1))return 0;return !C(e.size()-1);}

Code to test :

auto t = {
    "HATE",
    "LOVE",
    "POPULARIZE",
    "ACADEMY",
    "YOU",
    "MOUSE",
    "ACORN",
    "NUT",
    "AH",
    "STRONG",
    "FALSE",
    "PARAKEET"
};

for (auto&a : t) {
    std::cout << (s(a) ? "true" : "false") << '\n';
}

C++, 195 194 bytes

-1 bytes thanks to Zacharý

Uppercase, return true if input is a strong word, false otherwise ( C++ have simple int to bool implicit cast rules, 0 => false, true otherwise )

#include<string>
#define C(p)(v.find(e[p])==size_t(-1))
std::string v="AEIOUY";int s(std::string e){for(int i=0;i<e.size()-1;++i)if(e[i]>64&&e[i]<91&&C(i)&&C(i+1))return 0;return!C(e.size()-1);}

Code to test :

auto t = {
    "HATE",
    "LOVE",
    "POPULARIZE",
    "ACADEMY",
    "YOU",
    "MOUSE",
    "ACORN",
    "NUT",
    "AH",
    "STRONG",
    "FALSE",
    "PARAKEET"
};

for (auto&a : t) {
    std::cout << (s(a) ? "true" : "false") << '\n';
}