Conventionally in R one can use metacharacters in a regex with two slashes, e.g. ( becomes \(, but I find the same isn't true for square brackets.
mystring <- "abc[de"
#remove [,] and $ characters
gsub("[\\[\\]$]","",mystring)
[1] "abc[de"
[[:punct:]] works but I hate to use a non-standard regex if I don't have to. Can the regex set syntax be used?
You should enable perl = TRUE, then you can use Perl-like syntax which is more straight-forward (IMHO):
gsub("[\\[\\]$]","",mystring, perl = TRUE)
Or, you may use "smart placement" when placing ] at the start of the bracket expression ([ is not special inside it, there is no need escaping [ there):
gsub("[][$]","",mystring)
See demo
Result:
[1] "abcde"
More details
The [...] construct is considered a bracket expression by the TRE regex  engine (used by default in base R regex functions - (g)sub, grep(l), (g)regexpr -  when used without perl=TRUE), which is a POSIX regex construct. Bracket expressions, unlike character classes in NFA regex engines, do not support escape sequences, i.e. the \ char is treated as a a literal backslash char inside them. 
Thus, the [\[\]] in a TRE regex matches \ or [ char (with the [\[\] part that is actually equal to [\[]) and then a ]. So, it matches \] or [] substrings, just have a look at gsub("[\\[\\]]", "", "[]\\]ab]") demo - it outputs ab] because [] and \] are matched and eventually removed.
Note that the terms POSIX bracket expressions and NFA character classes are used in the same meaning as is used at https://www.regular-expressions.info, it is not quite a standard, but there is a need to differentiate between the two.
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