How can I make only one if-else statement among all of these?
If each ID1 can only have one valid corresponding ID2, then I would recommend using a  dictionary object to store the valid combinations, like this:

Dictionary&lt;string, string&gt; validIds = new Dictionary&lt;string,string&gt;();
validIds[ValidationFields.FO.ToString()] = ValidationTypes.P.ToString();
validIds[ValidationFields.FW.ToString()] = ValidationTypes.P.ToString();
validIds[ValidationFields.UF.ToString()] = ValidationTypes.P.ToString();
// ...


Then, you can check to see if the currently selected values are valid by simply comparing them to the valid combinations in the dictionary, like this:

if (validIds[ddlBr1Type.SelectedValue.ToString()] != ddlBr2Type.SelectedValue.ToString())
{
    BrkTypeValidator2.ErrorMessage = "'TOP0618 -Invalid combination of Bracket IDs'";
    args.IsValid = false;
}


By doing it that way, you only need the single if statement.  Another side benefit is that you can now store the list of valid combinations somewhere else, outside of your code, such as in a configuration file or a database.  Then you could load the data from that data source into the dictionary at run-time.