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Hasagat G'vul: The limits of Rabbi'ing in the Online World (Are there any?)
XIV. RELATIONSHIPS AMONG ORGANIZATIONS AND CONGREGATIONS, RABBIS AND OTHER PROFESSIONALS
C. Rabbis and their congregants should avoid inviting members of other congregations to join theirs. This avoids hasagat g’vul (improper crossing of political or economic boundaries) and the rancor that it causes.
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(יד) לֹ֤א תַסִּיג֙ גְּב֣וּל רֵֽעֲךָ֔ אֲשֶׁ֥ר גָּבְל֖וּ רִאשֹׁנִ֑ים בְּנַחֲלָֽתְךָ֙ אֲשֶׁ֣ר תִּנְחַ֔ל בָּאָ֕רֶץ אֲשֶׁר֙ יְהוָ֣ה אֱלֹהֶ֔יךָ נֹתֵ֥ן לְךָ֖ לְרִשְׁתָּֽהּ׃ (ס)

(14) You shall not move your countryman’s landmarks, set up by previous generations, in the property that will be allotted to you in the land that the LORD your God is giving you to possess.

(יז) אָר֕וּר מַסִּ֖יג גְּב֣וּל רֵעֵ֑הוּ וְאָמַ֥ר כָּל־הָעָ֖ם אָמֵֽן׃ (ס)
(17) Cursed be he who moves his fellow countryman’s landmark.—And all the people shall say, Amen.

. . . מִי שֶׁאֵינוֹ מַנִּיחַ אֶת הָעֲנִיִּים לִלְקֹט, אוֹ שֶׁהוּא מַנִּיחַ אֶת אֶחָד וְאֶחָד לֹא, אוֹ שֶׁהוּא מְסַיֵּעַ אֶת אֶחָד מֵהֶן, הֲרֵי זֶה גּוֹזֵל אֶת הָעֲנִיִּים. עַל זֶה נֶאֱמַר (משלי כב) אַל תַּסֵּג גְּבוּל עוֹלִים:

. . . One who does not allow the poor to gather gleanings, or one who allows one but not another, or one who helps one of them [to gather] behold he is a robber of the poor. Concerning him it is said: “Do not remove the landmark of those that come up.” (Proverbs 22:28).

אמר רב הונא האי בר מבואה דאוקי ריחיא ואתא בר מבואה חבריה וקמוקי גביה דינא הוא דמעכב עילויה דא"ל קא פסקת ליה לחיותי

Rav Huna said: A certain resident of an alleyway who set up a mill, and then another resident of the alleyway came and set up a mill next to his. The law is that he [the first one] may prevent him , as he can say to him: You are disrupting my livelihood.

לימא מסייע ליה מרחיקים מצודת הדג מן הדג כמלא ריצת הדג וכמה אמר רבה בר רב הונא עד פרסה שאני דגים דיהבי סייארא

Let us say that the following teaching offers support for his opinion: One must distance fish traps from fish, [i.e., from other fish traps] as far as the fish travels. Which is how much?

Rabba bar Rav Huna says: Up to a parasang [parsa].

[But, that is not a good support since] fish are different, as they look around.

אמר רב הונא בריה דרב יהושע פשיטא לי בר מתא אבר מתא אחריתי מצי מעכב ואי שייך בכרגא דהכא לא מצי מעכב בר מבואה אבר מבואה דנפשיה לא מצי מעכב

Rav Huna, son of Rav Yehoshua, says: It is obvious to me that a resident of one town can prevent a resident of another town [from establishing a similar business in the locale of the first individual]. But if he pays the tax of that first town, he cannot prevent him. The resident of an alleyway cannot prevent a resident of the same alleyway.

אמר רב יוסף ומודי רב הונא במקרי דרדקי דלא מצי מעכב דאמר מר עזרא תיקן להן לישראל שיהו מושיבין סופר בצד סופר

Rav Yosef said: And [even] Rav Huna [who said that a resident of an alleyway can prevent another from setting up an additional mill] concedes with regard to those who teach children that one cannot prevent another from working, as the Master said: Ezra instituted an ordinance for the Jewish people allowing that they establish one teacher alongside another teacher . . .

קנאת סופרים תרבה חכמה

Jealousy among teachers increases wisdom.

Scenarios
1. Rabbi A is a community-based rabbi and author who (before COVID) did a number of scholar-in-residence weekends with congregations. Over the years, he has built up an extensive contact list from those he has met in congregations. Now he is initiating a new entrepreneurial effort, creating an online center for adult Jewish learning. It will offer a number of asynchronous courses and also study sessions in real time during the lunch hour and on weekday evenings. When he sent out an announcement to his contacts, Rabbi B emailed to express alarm--the schedule of classes directly conflicts with her congregational offerings. Rabbi B points out that Rabbi A collected the names and emails of her congregants during a paid scholar-in-residence weekend. Is reaching out to those congregants now an example of hasagat gvul?
2. Rabbi C serves a small congregation on a part-time basis, leading shabbat services twice a month. Before COVID hit, the congregation offered lay-led services on the off weeks. When everything moved online, Rabbi C recommended that the community join in the Zoom services of a large congregation in another city. This large congregation is much better resourced with multiple clergy and professionally produced music at services. The large congregation announced that following COVID they will initiate a digital membership for people across the country who would like to continue joining them for services. Now Rabbi C fears that their congregants might quit their small congregation to join this large congregation digitally. Is offering digital membership to another rabbi's congregants an instance of hasagat gvul?
3. Several colleagues are in the planning stages of creating "The Schul Without Walls," a trans-geographic congregation that will offer shabbat and holiday services, daily meditation sits, classes and groups, all available online for a low membership fee. Members will also be eligible to pay premium fees for in-person life cycle officiation by regional rabbis on call.
The planners intend to affiliate with Reconstructing Judaism and have asked for help promoting their new congregation in movement-wide emails. Is this something the movement may promote or would that be hasagat gvul?