Is that a question? Because it looks a lot like an answer.
Sure you can use conditions.
Try this:
{if $item.type eq 'country'}
{$search_var = "profile_country = $country"}
{elseif $item.type eq 'state'}
{$search_var = "profile_state = $state"}
{/if}
{jrCore_list module="jrProfile" search1=$search_var order_by=$order_by template="profile_row.tpl"}
Try that.
If that doesnt work you might try putting back ticks around the $country / $state
{$search_var = "profile_state = `$state`"}
or perhaps squiggly brackets.
{$search_var = "profile_state = {$state}"}