Actually, Greeks and Russian Orthodox are very surprised when an inquirer comes into their church literally off the streets.
However, the True Orthodox, in my opinion, seem to be a little more kind and understanding. Well, that has been my experience as my husband and I look very Greek, so we have been accepted in no matter what church we have visited.
My Greek-in-laws have the impression that the Greek Orthodox Church is only intended for Greeks. They have apparently forgotten the Epistles of St. Paul to the Romans, the Hebrews, etc. Yes, Saint Paul did a tremendous outreach to the Greeks as shown in his Epistles to the Corinthians, etc.
Many Russian Orthodox will encourage visitors to attend other churches, thinking that the Russian Orthodox Church is only intended for those who speak Russian, but do they forget that the Slavic language alphabet was given to them by Saints Cyril and Methodius, who were Greek Orthodox? Church Slavonic is not fully understood by those who speak the modern dialect of Russian, as the Soviets disapproved of Church Slavonic and forced Russian on all Slavic countries that they had conquered.
Several priests have told me that those in True Orthodox Parishes where there are a lot of converts tend to shower more love on inquirers. Those parishes that have been insulated from outsiders generally do not have any outreach to the non-Orthodox except for the relatively few outsiders who have fallen in love, and then have converted to Orthodoxy in order to marry one of their parishioners, Then they become part of the family and are no longer outsiders. However, if the priest is a convert, then he may try by his sermons to help the parish overcome any lack of a missionary zeal. He may even try an outreach, but without the support of the parish council, any outreach is likely to fail as it takes financial support from parishioners,, especially the parish council.
Anyway, the best True Orthodox parishes are those with lots of converts because there you will find families who are more accepting of those who are seeking to convert from Roman Catholicism, Protestantism, Judaism, Islam, Buddhism, etc. In those parishes, you most likely will find inter-racial families: Hispanics, Lebanese, Japanese, Chinese, Blacks, Filipinos, Native Americans, etc.