Berakhot 028

7:
Rabbi Me'ir was a younger contemporary of Rabbi Yehudah ben-Ilai, who is in dispute with him in this mishnah. They were active during the tumultuous middle decades of the 2nd century CE, during and after the disastrous Bar-Kokhba insurrection. Rabbi Me'ir was one of the principle halakhic influences on Rabbi [Yehudah ha-Nasi], the compiler of the Mishnah – indeed, Rabbi Me'ir's personal 'mishnah' may have been the foundation for Rabbi's.

8:
Our mishnah distinguishes between a greeting offered by someone else to a person engaged in reciting the Shema, and a greeting offered by the reciter himself or herself. To understand our mishnah we must also distinguish between the text of the Shema (and its berakhot) and the intervals between the parashot, or paragraphs. A further distinction is the standing of the person offering or receiving the greeting: is it someone the reciter owes common politeness to or is it someone to whom he or she owes much greater respect? – particularly (but not exclusively) someone in authority.

9:
Rabbi Me'ir's view is as follows: if the reciter is at a break between paragraphs when someone must be greeted or a greeting must be returned, then there is no restriction. However, he says, if the reciter is in the middle of a paragraph he or she should only offer a greeting or respond to a person who deserves our respect. [The Hebrew term Yir'ah does not always indicate "fear" alone, but more often – in rabbinic Hebrew – it denotes what we would now call respect.] Rabbi Yehudah has a more elaborate view: if the reciter is in the middle of a paragraph he or she may initiate a greeting only to a person who has our respect, whereas they may return a greeting out of common politeness. If the reciter is between paragraphs he or she may initiate or respond to a greeting even to someone to whom we don't even have to be polite.

10:
Accepted halakhah is as follows [based on Shulĥan Arukh, Oraĥ Ĥayyim 66]:

Between the paragraphs one may offer a greeting to someone "important" and one may respond to any person's greeting. In the middle of the paragraphs one may offer a greeting to someone deserving of our respect (or more) and respond to the greeting of someone "important".

Examples given of "someone deserving of our respect (or more)" include a parent, one's rabbi, anyone more learned than we are, persons in public authority and people we are actually afraid might do us some violence. I think that from these hints everyone can make their own personal extrapolations. Nowadays, "someone important" would include most adults, I think.

11:
The concept "between the paragraphs" indicates the following: between the first and second berakhot of the Shema; between the second berakhah and the first paragraph of the Shema itself; between the first and second paragraphs of the Shema itself; and between the second and third paragraphs of the Shema itself. However, the junction between the end of the third paragraph of the Shema itself and the beginning of the berakhah that comes after the Shema is not considered to be an interval between paragraphs, but "in the middle of a paragraph".

12:
What we have said so far is concerned with interruptions that disturb concentration. It does not apply to a silent waiting. When worshipping in public, the custom is to conclude the third paragraph of the Shema itself and to add the first word of the next berakhah, emet; it is then quite permissible to wait in concentrated silence for the cantor, and then to continue with the berakhah that comes after the Shema.