Is using "and/or" recommended for formal writing, or is it frowned upon?
I believe most style books advise against using and/or in formal writing. By "formal" I mean in newspapers or novels. If space is extremely limited, most writers would have no qualms about it, as in dictionary entries or footnotes.
The reason is that or can mean either "either A and not B, or B and not A" or "A or B or both" in ordinary language: 99 % of the time, readers will be able to figure out whether it is used inclusively or exclusively based on context. If ambiguity could arise, the writer should add some context to make it clear:
This test may be taken on June 5 or July 12.
May the test be taken twice? There are several ways to clarify this, though not every way may work in any situation. Suppose the answer was yes:
This test may be taken on June 5 and July 12 [this may still not be clear in some cases].
This test may be taken twice, on June 5 and July 12.
This test may be taken on June 5, and again on July 12.
This test may be taken on June 5 or July 12, or on both dates.
Suppose the test might be taken only once:
This test may be taken on either June 5 or July 12 [this may still not be clear in some cases].
This test may be taken once, on June 5 or July 12.
This test may be taken on June 5 or July 12, but not on both dates.
Etc.
And/or is, in the vast majority of contexts, redundant. It's a construct that has become lexicalized and has evidently [come under intense criticism][1].
Take the following example
Please mail and/or FAX your reply.
This type of construct is extremely common, but what does this sentence mean? Either I will send my reply by mail, or I will send it by FAX, but I can not do both, so why the "and"?
I suggest using or where there are options from which you should pick only one and simply explain that multiple options are possible from a list when introducing it. As in the preceding sentence, only use and when both apply.
Regarding your specification of "formal writing": if you are writing for a specific audience or body, consult their style manual and employ it as gospel regardless or your (or my) preferences.