Without really knowing what your conditions are checking, I think I would usually move that check to within the method that actually relates to getting foo or bar. It seems like a case of your one method doing more than it's supposed to.

A different approach:

var fooTask = GetFoo();
var barTask = GetBar();

await Task.WhenAll(new [] { fooTask, barTask });
result.foo = (await fooTask) ?? result.foo;
result.bar = (await barTask) ?? result.bar;

// ...
async Task<string> GetFoo()
{
    if (!myCondition) {
        return Task.FromResult((string)null);
    }
    return await DoHeavyWorkFoo();
}

async Task<string> GetBar()
{
    if (!myOtherCondition) {
        return Task.FromResult((string)null);
    }
    return await DoHeavyWorkBar();
}

One way to do this is to have two lists, one list of tasks and one list of actions. The actions will be invoked sequentially after the completions of all tasks, and will assign the properties of the result object. Example:

var tasks = new List<Task>();
var actions = new List<Action>();
var result = new MyClass();

if (myCondition)
{
    var task = getAsync();
    tasks.Add(task);
    actions.Add(() => result.Foo = task.Result);
}

if (myOtherCondition)
{
    var task = getAsync2();
    tasks.Add(task);
    actions.Add(() => result.Bar = task.Result);
}

await Task.WhenAll(tasks);

actions.ForEach(action => action());

This way you don't need to store each Task in a separate variable, because each lambda expression captures the task variable in the inner scope of the if block. When the Action is invoked, the task will be completed, and so the task.Result will not block.

Just for fun: If you want to get fancy, you could encapsulate this "parallel object initialization" functionality in an ObjectInitializer class, that would invoke all the asynchronous methods concurrently, and then create a new object and assign the value of each of its properties sequentially:

public class ObjectInitializer<TObject> where TObject : new()
{
    private readonly List<Func<object, Task<Action<TObject>>>> _functions = new();

    public void Add<TProperty>(Func<object, Task<TProperty>> valueGetter,
        Action<TObject, TProperty> propertySetter)
    {
        _functions.Add(async arg =>
        {
            TProperty value = await valueGetter(arg);
            return instance => propertySetter(instance, value);
        });
    }

    public async Task<TObject> Run(object arg = null)
    {
        var getterTasks = _functions.Select(f => f(arg));
        Action<TObject>[] setters = await Task.WhenAll(getterTasks);
        TObject instance = new();
        Array.ForEach(setters, f => f(instance));
        return instance;
    }
}

Usage example:

var initializer = new ObjectInitializer<MyClass>();
if (myFooCondition) initializer.Add(_ => GetFooAsync(), (x, v) => x.Foo = v);
if (myBarCondition) initializer.Add(_ => GetBarAsync(), (x, v) => x.Bar = v);
MyClass result = await initializer.Run();