I can tell you that most of them don't know anything about it. I grew up Baptist, and I'm honestly not sure what other Protestants think when they hear the words "Orthodox Christian", but I don't think it's very good.
I first heard it out of my father's mouth just over a year ago, when he was sharing with us what he had found whilst really digging into biblical truths. Then, a month or two later, I met my now Fiancé and I was able to ask endless questions, which he answered graciously and thoroughly, allowing me to do my own informed reading and come to my own conclusions.
I was keen to learn, and my mother was skeptical. She did warm right up after a couple of months. She doesn't intend to join Orthodoxy in an official sense, though she follows the prayers and (against recommendation, not having a priest for guidance) most fasts, along with live streaming most weekly services from various parishes and time zones! Sometimes she will watch three or four separate services of various Orthodox and Protestant types on a single Sunday morning. Meanwhile, my elder sister is a proud Five Point Calvinist and calls it "Orthodox brain rot".
When my parents told some of their friends at church that they were looking into it, there was quite a bit of attempted dissuasion, including sending articles and charts (written and compiled by unfortunately misinformed fellow Protestants), covered with many of their own notes as well, showing how Orthodoxy was 'actually just as sinful and terrible as Catholicism!' among many other arguments that held little merit and were improperly understood by the writer. I myself had a couple of friends doing their own researching and coming to tell me that they were worried (and convinced that) I was straying from God and following shrouded lies of the devil.
Putting all that together on 'paper' makes me realize how much God has had a hand in guiding my family towards Orthodoxy! I hadn't thought about how much resistance others have given us.
So, perhaps the folks inviting you to their churches even think they are doing you a service!
A few people have been academically curious, but I'm not sure why many of them are so nervous about Orthodoxy.