Quotes should be quotes
If a user quotes material incorrectly, then it should be corrected. If the difference was intentional then it needs to be very clear what change was made (usually restricted to the very common "emphasis mine" or ellipses to reduce irrelevant information). Switching between "and" and "&" is unlikely to be harmful, but if something is represented as a quotation then it should be identical to the source including stylistic choices. There is some ambiguity if the quotation is from a spoken source, in which case different transcriptions might have different formatting.
The only time I might not be inclined to "repair" an inaccurate quotation through editing is if the quotation is in a question and that question depends on the inaccuracy so the answer to the question is "your quote is inaccurate".
"&" is not incorrect English
"&" might not strictly be "common" in either formal or informal English, but it is an entirely valid stylistic choice and there's no reason to edit it out or admonish its users. Unless you can point out specifically harm that occurs specifically because of the ampersand symbol appearing at a certain frequency, it should be left alone. There are some situations where only one is correct, mostly related to Quotes and similar concepts like the names of businesses, but otherwise neither version is problematic and there's no need to unify this stylistic choice across the site.