Perhaps we can apply Rambam's approach in Hilchos Mamrim 3:3
בַּמֶּה דְּבָרִים אֲמוּרִים בְּאִישׁ שֶׁכָּפַר בַּתּוֹרָה שֶׁבְּעַל פֶּה בְּמַחֲשַׁבְתּוֹ וּבִדְבָרִים שֶׁנִּרְאוּ לוֹ. וְהָלַךְ אַחַר דַּעְתּוֹ הַקַּלָּה וְאַחַר שְׁרִירוּת לִבּוֹ וְכוֹפֵר בַּתּוֹרָה שֶׁבְּעַל פֶּה תְּחִלָּה כְּצָדוֹק וּבַיְתּוֹס וְכֵן כָּל הַתּוֹעִים אַחֲרָיו. אֲבָל בְּנֵי הַתּוֹעִים הָאֵלֶּה וּבְנֵי בְּנֵיהֶם שֶׁהִדִּיחוּ אוֹתָם אֲבוֹתָם וְנוֹלְדוּ בֵּין הַקָּרָאִים וְגִדְּלוּ אוֹתָם עַל דַּעְתָּם. הֲרֵי הוּא כְּתִינוֹק שֶׁנִּשְׁבָּה בֵּינֵיהֶם וְגִדְּלוּהוּ וְאֵינוֹ זָרִיז לֶאֱחֹז בְּדַרְכֵי הַמִּצְוֹת שֶׁהֲרֵי הוּא כְּאָנוּס וְאַף עַל פִּי שֶׁשָּׁמַע אַחַר כָּךְ [שֶׁהוּא יְהוּדִי וְרָאָה הַיְהוּדִים וְדָתָם הֲרֵי הוּא כְּאָנוּס שֶׁהֲרֵי גִּדְּלוּהוּ עַל טָעוּתָם] כָּךְ אֵלּוּ שֶׁאָמַרְנוּ הָאוֹחֲזִים בְּדַרְכֵי אֲבוֹתָם הַקָּרָאִים שֶׁטָּעוּ. לְפִיכָךְ רָאוּי לְהַחְזִירָן בִּתְשׁוּבָה וּלְמָשְׁכָם בְּדִבְרֵי שָׁלוֹם עַד שֶׁיַּחְזְרוּ לְאֵיתָן הַתּוֹרָה
To whom does the above apply? To a person who denied the Oral Law consciously, according to his perception of things. He follows after his frivolous thoughts and his capricious heart and denies the Oral Law first, as did Tzadok and Beitus and those who erred in following them.
The children of these errant people and their grandchildren whose parents led them away and they were born among these Karaities and raised according to their conception, they are considered as a children captured and raised by them. Such a child may not be eager to follow the path of mitzvot, for it is as if he was compelled not to. Even if later, he hears that he is Jewish and saw Jews and their faith, he is still considered as one who was compelled against observance, for he was raised according to their mistaken path. This applies to those who we mentioned who follow the erroneous Karaite path of their ancestors. Therefore it is appropriate to motivate them to repent and draw them to the power of the Torah with words of peace.(Touger translation my emphasis)
So arguably, one could make the case that since those of Karaite origin are regarded as a תִינוֹק שֶׁנִּשְׁבָּה and it is therefore fitting to try and draw them closer to Torah, it might be considered okay to engage in some form of dialogue if it will have the desired effect. However, I would assume that if the person engaging in the conversation might become enamoured with the Karaite tradition, and want to pursue it themselves, then this should obviously be avoided.
Indeed, in terms of the Hashkafic perspective, it is interesting to note the Wikipedia page on Rav Soloveitchik as saying:
Soloveitchik was a life-long critic of all forms of non-Orthodox Judaism, including Reform Judaism and Conservative Judaism. He believed that these denominations were in significant error where they differed from Orthodox Judaism. He compared religious dialogue with Reform and Conservative leaders to dialogue between Pharisees and Karaites, considering it ridiculous.
So possibly if we read between the lines, it would seem at least to Rabbi Soloveitchik's view that such dialogues should be avoided.