Are Greek Orthodox generally okay with Catholics attending their Vespers?
You’ve asked about Vespers.I’d say yes.
I can’t say I have as much experience with Greek Orthodox Vespers as it sounds like the others who have posted have had. I get to Vespers, Matins, Bridegroom services etc. at the nearby Greek Orthodox Cathedral maybe 15 times a year. As a Russian Catholic I prefer going to OCA where the translation and the music is the same as what we use, or the ROCOR where the music is the same, tho no English which for me is a problem.
The last Matins I went to at the Greek Orthodox Cathedral I was the only person there, along with the priest who was the cantor, for the first 40 minutes. By the end of the service there were maybe a dozen people in the pews. I’d say the average attendance for Matins or Vespers at this cathedral is 12-19 people. When I’ve been in services in the SF Greek Cathedral and another local parish, all those have been a major feast like their altar feast or a Hirerchical Liturgy, so those were very well attended,
My point is that Vespers has a small attendance at the Greek Orthodox Churches around here. In talking with friends in the clergy that seems pretty typical for Greeks here. So with so few people there, people will likely notice you are not a regular parishioner and may well speak to you. **I can’t tell you how many times at the Greek Churches when chatting and the inevitable question comes up “So, what is your parish?” and I say the name of my parish and that I’m Eastern Catholic, the reply was “We all the same!”. ** (I’ve never heard that reply from Russians, LOL) I’m sure the local pastor can have some influence on how people respond but here in a very large metropolitan area people are used to all kinds of people showing up. If you are well behaved you’re likely to find yourself warmly welcomed.
All the Greek Orthodox services I’ve been in were primarily in Greek, with however a fair amount of repetition in English, except for the Orthodox Christian Fellowship here which uses the GOARCH English translations and no Greek, tho Greek Orthodox celebrants, The Cathedral has handouts for some services like those during Great Lent, which give the English translations if the service is largely in Greek.
My UGCC parish does not offer Saturday Night Vespers. Less than a mile from my house is a Greek Orthodox parish that does (GOA-Ecumenical Patriarchate). I mean if someone in the congregation asks who I am, would they freak if I tell them I’m a Greek Catholic?
Around here both clergy and the faithful seem to actually appreciate it that we who are there care enough to attend the services. There are Catholics attending services and Divine Liturgy quite often in Orthodox parishes. Your situation is a typical reason for this. We in my parish have the same issue and a number of us are in the ROCOR or OCA parishes Saturday nights. I only go to the Greek Church if it’s a week with a number of services and driving an hour every night is just too much, when the Greek Church is only a 20 minute drive and no bridge toll.

But I am there often enough to still feel at home there and be well known to all the clergy and to a number of those few who do attend these Vespers and Matins services.
Let us know how it goes.
