If you're okay with passing the types as generic arguments, there is a solution. Unfortunately, C# doesn't support variadic generics. You have to define the function for each generic arity.
public static bool IsOfType<T>(this object obj) => obj is T;
public static bool IsOfType<T1, T2>(this object obj) => obj is T1 || obj is T2;
public static bool IsOfType<T1, T2, T3>(this object obj) => obj is T1 || obj is T2 || obj is T3;
public static bool IsOfType<T1, T2, T3, T4>(this object obj) => obj is T1 || obj is T2 || obj is T3 || obj is T4;
public static bool IsOfType<T1, T2, T3, T4, T5>(this object obj) => obj is T1 || obj is T2 || obj is T3 || obj is T4 || obj is T5;
public static bool IsOfType<T1, T2, T3, T4, T5, T6>(this object obj) => obj is T1 || obj is T2 || obj is T3 || obj is T4 || obj is T5 || obj is T6;
public static bool IsOfType<T1, T2, T3, T4, T5, T6, T7>(this object obj) => obj is T1 || obj is T2 || obj is T3 || obj is T4 || obj is T5 || obj is T6 || obj is T7;
public static bool IsOfType<T1, T2, T3, T4, T5, T6, T7, T8>(this object obj) => obj is T1 || obj is T2 || obj is T3 || obj is T4 || obj is T5 || obj is T6 || obj is T7 || obj is T8;
I doubt you'll need more than 8 types but if you do, just define more overloads.