MySQL's regular expressions support a metacharacter class that matches word boundaries:
SELECT ...
FROM mytable
WHERE member_ids REGEXP '[[:<:]]1[[:>:]]'
See http://dev.mysql.com/doc/refman/5.6/en/regexp.html
If you don't like that, you can search using a simpler regular expression, but you have to escape the pipes because they have special meaning to regular expressions. And you also have to escape the escaping backslashes so you get literal backslashes through to the regular expression parser.
SELECT ...
FROM mytable
WHERE member_ids REGEXP '\\|1\\|'
You can do this in one expression if you modify your strings to include a delimiter at the start and the end of the string. Then you don't have to add special cases for beginning of string and end of string.
Note this is bound to do a table-scan. There's no way to index a regular expression match in MySQL. I agree with @MichaelBerkowski, you would be better off storing the member id's in a subordinate table, one id per row. Then you could search and sort and all sorts of other things that the pipe-delimited string makes awkward, inefficient, or impossible. See also my answer to Is storing a delimited list in a database column really that bad?