HOWEVER… Rabbi Eliezer Wenger zatzal (a Lubavitcher Hasid) wrote as follows:
B’er Haitev in Siman 124:4
quotes an opinion that states that it is not necessary to protest against
anyone that is learning or saying Tachanun [penitential prayers] during the
repeetition of the Amidah provided that they concentrate by the end of each
of the blessings to answer Amen; however, there are those that disagree and
disallow it totally.
I find it interesting that the Lubavitcher would even mention the opinion that says not to protest, when the “Alter Rebbe” writes the exact opposite (see my previous comment).