In light of the answers given here Responding to kaddish in pesukei dezimro can anyone explain why the popular minhag is to answer brich hu at the kaddish before shmone esrei at maariv? There is semichat geulah letefilla which seems to be at least as serious as pesukei dezimra. Sources always appreciated.
Thank you everyone for your insight. I just thought I'd point out one other possibility: the "in hachi nami." Towards the end of this article, R Ari Enkin quotes R Mordechai Willig of YU to specifically not answer brich hu at maariv in the kaddish before shmoneh esrei. This is indeed also my practice.
EDIT: I now have (circumstantial) evidence that Rav Joseph B. Soloveitchik held this way as well. See this pdf of Friday night services that claims to be according to his nussach. You'll notice that in all the kaddishes it says to say "brich hu" except the kaddish before shmoneh esrei at maariv! It seems he felt answering then was an interruption and not permitted.
I don't have a source, this is just logical to me. Any feedback would be appreciated.
Kaddish is a tzibur prayer that was instituted to be said by a designated leader (shatz). When the tzibbur listens to that prayer, they are included. If, after saying shmei d'kudsha, the chazan praises "brich hu", it should not be any more of a hefsek if the congregation praises brich hu as well.
It is probably distinguished from the rest of kaddish said by the shatz (Yisgadal, yisbarach) because it is almost parenthetical. The Shatz praised "His holy name", we say brich hu.
This is different than Baruch hu uvaruch shemo during pesukei d'zimra where the praise is not a pasuk of zimra, whereas here, the brich hu is integral to the kaddish, which is, of course, not a hefsek.
This is also different than mixing hearing a bracha with saying a bracha (like kiddush, which is problematic acc. to some) since there is no requirement to personally say the kaddish, it just needs to be said.
See MB 236 (2)  who explains (my translation; my additions in brackets) that our custom to interpose pesukim of (“Boruch HaShem leolom omain veomain” and) “yiru eineinu” and “kaddish” is because in the earlier times their shuls were in the fields and they were frightened to remain there until the time of davenning (=finishing) maariv. So they instituted to say these pesukim which correspond to the 18 mentions of HaShem’s name in the maariv Amidah (and they omitted the maariv Amidah) and they finished and left after they had said kaddish.
And now that that we have reinstituted to daven (the Amidah of) maariv in our shuls, we did not remove the original minhag. Nevertheless one must not interrupt with anything else. And there were some Gedolim who had the minhag not to say these pesukim.
IMHO, we see from the MB that the kaddish is part of the original minhag and was said after “Boruch HaShem leolom omain veomain” which was the substitute for the maariv Amidah. There would have been no problem in responding “brich hu” to this kaddish and this is part of the minhag that has not been removed. I think this is what the MB means by “Nevertheless one must not interrupt with anything else.” He implies that this is in a sense an interruption but permitted because of the original minhag.