你只需要调用Activate一次。你可以通过一个静态构造函数来实现：

public static class ProcessQueueForIntercom
{
    static ProcessQueueForIntercom()
    {
        MapInitializer.Activate();
    }

    [FunctionName("ProcessQueue")]
    public static void Run([QueueTrigger("messages")]string myQueueItem, TraceWriter log)
    {             
        // rest of the code
    }
}

或者只在MapInitializer本身上创建一个静态构造函数。
另请参阅this answer。

由于静态Mapper.Initialize API现在已经正式失效，我认为最好的解决方案是在函数类构造函数中注入一个Map器。

using AutoMapper;
using Microsoft.Azure.Functions.Extensions.DependencyInjection;
using Microsoft.Extensions.DependencyInjection;
using YourNamespace.Models;

[assembly: FunctionsStartup(typeof(YourNamespace.Startup))]

namespace YourNamespace
{
    class Startup : FunctionsStartup
    {
        public override void Configure(IFunctionsHostBuilder builder)
        {
            var mappperConfig = new MapperConfiguration(cfg =>
                {
                cfg.CreateMap<User, UserResponse>(); 
                // you can have the maps in a dedicated Profile subclass if you like
            });
            builder.Services.AddSingleton(mappperConfig.CreateMapper());
        }
    }
}

然后，将自动Map器注入到函数类中，如下所示：

public class UsersApi
{
    private readonly IMapper _mapper;

    public UsersApi(IMapper mapper)
    {
        _mapper = mapper; 
    }

    [FunctionName(nameof(UsersApi.GetUser))]
    public async Task<IActionResult> GetUser(
        [HttpTrigger(AuthorizationLevel.Anonymous, "get", Route = "users/{id}")] HttpRequest req,
        ILogger log,
        string id)
    {
        User user = await UserRepository.GetUser(id);
        UserResponse res = _mapper.Map<UserResponse>(user);
        return new OkObjectResult(res);
    }
}