Redirect stderr to /dev/null

Just move the redirection to the first command, i.e.

find ... 2>/dev/null | xargs ...

Or you can enclose everything in parenthesis:

(find ... | xargs ...) 2>/dev/null

In order to redirect stderr to /dev/null use:

some_cmd 2>/dev/null

You don't need xargs here. (And you don't want it! since it performs word splitting)

Use find's exec option:

find . -type f -name "*.txt" -exec grep -li needle {} +

To suppress the error messages use the -s option of grep:

From man grep:

-s, --no-messages Suppress error messages about nonexistent or unreadable files.

which gives you:

find . -type f -name "*.txt" -exec grep -lis needle {} +