Bash : command line with optional arguments

tar -czf backup.tgz "$exclude1" "$exclude2" ${exclude3+"$exclude3"} 2>&1

${exclude3+"$exclude3"} expands to nothing, if $exclude3 is unset, and to "$exclude3", if it is set.

(and similarly for the other variables that are potentially unset.)

Note that there is a difference between an unset variable and a variable that is set to the empty string, so you should use

unset exclude3

instead of

exclude3=''

Since you're working in bash, use an array.

excludes=()
excludes+=('--exclude=/path/*')
…
tar -czf backup.tgz "${excludes[@]}"

If you have an optional entry in some variable, add it in a conditional.

if [[ -n $exclude_or_empty ]]; then excludes+=("$exclude_or_empty"); fi

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