Ok, if anybody has encountered the same problem, here's the workaround I found for it.

Code from the "Register Member" snippet [NOT WORKING]

    @if (registerModel.MemberProperties != null)
    {
        for (var i = 0; i < registerModel.MemberProperties.Count; i++)
            {
                @Html.LabelFor(m => registerModel.MemberProperties[i].Value, registerModel.MemberProperties[i].Name)

                @Html.EditorFor(m => registerModel.MemberProperties[i].Value)
                @Html.HiddenFor(m => registerModel.MemberProperties[i].Alias)
                <br />
            }
    }

Instead of looping through the MemberProperties array with the index i, I was able to access the properties by retrieving them one by one. I used the actual index number instead of the variable i.

New code [WORKING]

    @if (registerModel.MemberProperties != null)
    {
        // first property
        @Html.LabelFor(m => registerModel.MemberProperties[0].Value, registerModel.MemberProperties[0].Name)

        @Html.EditorFor(m => registerModel.MemberProperties[0].Value)
        @Html.HiddenFor(m => registerModel.MemberProperties[0].Alias)
        <br />

        // second property
        @Html.LabelFor(m => registerModel.MemberProperties[1].Value, registerModel.MemberProperties[1].Name)

        @Html.EditorFor(m => registerModel.MemberProperties[1].Value)
        @Html.HiddenFor(m => registerModel.MemberProperties[1].Alias)
        <br />

        // ... and so on for all the other MemberProperties defined in my MemberType
        }
    }

For some reason, the for loop was adding the prefix "CS$<>8__locals1" to all of the properties attributes. The Alias of the properties passed by the registration form didn't match the Alias of the properties defined in the MemberType.

With this fix, the Alias match and the values of the properties are correctly saved on the new member created.