Per Daniel's comment: The phrase "tacit consent" pretty much covers the intended meaning. Also, "speak now or forever hold your peace," from the standard wedding ceremony is similar. Jocularly, the auctioneer's "going once, going twice..." can be used conversationally as well.

"Avoidancing" was coined for this.

This may be an acceptable term. I fully understand the remarks above, that "mail" in and of itself should be sufficient. However, we have two major operations - one involving email and one concerning snail mail, and it is necessary to sharply mark the difference. Any possibility of confusion needs to be eliminated. Thank you for your answer.

Nice, comprehensive answer.

Correct. The standard injunction to avoid using conjunctions (or conjuncts) at the beginning of a sentence was predicated on the assumption that such sentences tended to be fragments. In fact, as this matter has subsequently been reviewed over the past 60 years or so, the concern has been found to be wholly unwarranted. The so-called "rule" is a shibboleth and can be ignored as being an exemplar of Ted Bernstein's "Miss Thistlebottom's Hobgoblins."

This is my field, and I'm unaware of any guidance from style manuals on this question. Rather, this is a situation requiring judgement and editorial skill. F'x gives proper advice above.

If you want to be totally inclusive, the broader term is "LGBTQIA" (lesbian, gay, bisexual, transgender, questioning, intersex, and asexual). The difficulty arises in that these initialisms aren't readily pronouncable. A common shorthand you do hear is "gay or straight," to mean homo- or heterosexual, implying that gay can include lesbian in standard discourse. If you are addressing a largely or significantly non-traditional audience, then LGBT, LBGQT, etc., may be preferred.

+1 on Joe Bob Briggs being the source. I thought I was going to be the first one with this cite. Well done, Brendon.

A double negative, as in the quoted instance, is known as an "informal intensifier." Logically, it doesn't hold up, but in practice, it stresses the negative quality in question.