>>This works as well for me:
>
>Text not NText.

Still working fine:

drop table #test
go
create table #test(Subject_E text)

insert into #test (Subject_E) values ('Testing [OldMemberTableName]'), ('Testing [OLDMEMBERTABLENAME]')

UPDATE #test SET Subject_E=replace(cast(Subject_E as varchar(max)) ,'[OldMemberTableName]','[Member]')
select * from #test

Please check what is the database collation and do you have collation for that column. Script both database and the table.