How can I get bash/zsh to change some text from “foo.foo.foo” to “foo foo foo” with a script/alias?

You can use tr command to convert character.

% echo "foo.foo.foo" | tr '.' ' ' 
foo foo foo

Using pure bash:

bash-3.2$ a='a.a.a'
bash-3.2$ echo "${a/./ }"
a a.a
bash-3.2$ echo "${a//./ }"
a a a

Using Internal Field Separator (IFS) variable:

bash-4.3$ old_ifs=$IFS
bash-4.3$ IFS="."
bash-4.3$ var="foo.foo.foo"
bash-4.3$ echo $var
foo foo foo
bash-4.3$ IFS=$old_ifs

This can be put nicely into a function:

split_dot()
{

    string="$1"

    if set | grep -q "IFS";
    then
       ifs_unset="false"
       old_ifs=$IFS
    else
       ifs_unset="true"
    fi

    IFS="."
    echo $string
    if [ "$ifs_unset" == "true" ];
    then
       unset IFS
    else
       IFS=$old_ifs
    fi
}

And run as so:

bash-4.3$ split_dot "foo.baz.bar"                                                                             
foo baz bar

Anyone missed awk/perl/python/go:

% awk '{gsub(/[.]/, " ", $0); print}' <<<'foo.foo.foo'                      
foo foo foo

% perl -pe 's/\./ /g' <<<'foo.foo.foo'                                      
foo foo foo

% python -c 'import sys; print sys.stdin.read().replace(".", " ")' <<<'foo.foo.foo'
foo foo foo

% cat input.go
package main

import (
    "os"
    "strings"
    "fmt"
)

func main () {
    args := os.Args
    if len(args) != 2 {
        fmt.Println("Not enough arguments")
        return
    }
    out := strings.Replace(args[1], ".", " ", -1)
    fmt.Println(out)
}

% go run input.go 'foo.foo.foo' 
foo foo foo