Let us start by exploring why Ashkenazim refrain from doing Birkat Kohanim daily in chutz la’aretz and see whether it is possible for you to participate in the Sephardi minyan’s practice. According to the original halacha, Birkat Kohanim is said every day. However, at least 700 years ago, the minhag developed in most Diaspora communities not to do it on weekdays, but to rather limit it to Yom Tov (and perhaps Shabbat). The Shulchan Aruch[2] rejected this minhag, which explains the prevalent (although not universal) Sephardic practice, but the Rama[3] and Ashkenazim accept it.
Many explanations have been suggested for the minhag, which is often a sign that no individual reason is particularly compelling. We will mention a few conjectures.
The Rama remarks that one should recite the blessings of Birkat Kohanim when in a good mood, which happens more often on Yom Tov. The Maharil[4] and the Agur[5] cite concern that the time spent on Birkat Kohanim leads to difficulty for those who need to get to work. In addition, the Maharil[6] suggests that a practice developed that one must be ritually pure to do Birkat Kohanim, and since it is not always practical for kohanim to go to the mikveh, it became customary to omit Birkat Kohanim entirely. The Beit Yosef[7] reacted that it is illogical to use a post-Talmudic stringency to require ritual purification before Birkat Kohanim as a reason to circumvent the mitzva. While conceding that the absolute obligation to do Birkat Kohanim applies only when the congregation calls upon the kohanim, which does not occur according to the minhag, the Beit Yosef maintains that it is still wrong to avoid the mitzva.
There are other explanations for the minhag as well. The Beit Ephrayim[8] says that since the reliability of a kohen’s genealogy is no longer strong, we minimize the practice of Birkat Kohanim to avoid the prohibitions involved in a non-kohen performing the mitzva. (If we avoided Birkat Kohanim entirely, genuine kohanim might stop observing the restrictions of a kohen, which is a bigger concern, and we therefore maintain the practice on Yom Tov.) The Chatam Sofer[9] explains that we usually lack the proper level of concentration during davening that is necessary to incorporate Birkat Kohanim into the tefilla. Additional reasons are advanced,[10] but this will have to suffice in this forum.
Several Ashkenazi poskim (most prominently the Gra) yearned to return to the daily practice of Birkat Kohanim and did not think that any of the reasons suggested justified uprooting the practice. Nevertheless, the idea of changing this old minhag is problematic. (Some frightening stories of failed attempts to restore the practice can be found in the Minchat Yitzchak[11] and the Aruch HaShulchan.[12] These stories lead many to feel that it is apparently divinely desired that we not change the minhag.) However, there are no qualms expressed regarding communities that have always followed the standard halacha of doing Birkat Kohanim daily. We also note that the minhag is that kohanim from chutz la’aretz join in Birkat Kohanim daily when they are in Israel.[13]
Some of the explanations that we have seen apply primarily to a community not doing Birkat Kohanim but do not preclude an individual from joining an existing Birkat Kohanim. Of supreme importance in this context is that if a kohen is present during a communal call to the kohanim, he has a Torah obligation to take part in Birkat Kohanim, whereas the minhag was likely instituted based on the idea that the kohanim would not be called at all.[14] A solution, if necessary, is for the Ashkenazi kohen to step out beforehand. (We do not feel it is justifiable to tell an Ashkenazi not to daven with Sephardim.) However, any public action that separates one from what the shul is doing is itself very problematic. In general, one should follow the local practice (including the tradition of the davening in the shul that one attends) regarding matters that are noticeable to the public.[15] For this reason, for example, the Chayim Sha’al[16] allows a Sephardi to recite a beracha on Hallel on Rosh Chodesh if he is davenening in an Ashkenazi minyan,[17] and the Divrei Yatziv[18] writes similarly regarding the haftara at Mincha of a fast day. Therefore, we feel that it is proper for an Ashkenazi kohen to do Birkat Kohanim along with the other kohanim at a Sephardi minyan.