Actually there was an interview taken sometime back where Ben Daniels comments about this. Here is the quote:
"Marcus’s sexuality, whatever it may turn out to be, has no shame attached to it. It doesn’t bother him. He doesn’t see it as a sin. I think Marcus, as well as having his own version of the Bible, has his own version of Catholicism! I like the idea that, if we progress into a Season 2, his sexuality is something that will be explored further. Because he no longer has his collar, which means he is free from all the priestly vows that he is taken."
"I feel that he has always been someone who is attracted to people’s minds and their stories, regardless of gender and sexuality. To suddenly be able to interact with people in a physical way will be a very new and exciting thing for him. He was institutionalized from a very young age and to suddenly be free of all that — I think he might turn into a 52-year-old teenager!"
"I think at the moment his sexuality could be very fluid. I know everyone online things he is gay because he flirted with a man in a bar — but hey, this is “The Exorcist”… It could go any which way! It could get fantastically messy!"--- https://www.google.co.in/amp/screenertv.com/television/the-exorcist-season-1-finale-ben-daniels-interview/amp/
Although I didn't list this specific option above, I strictly fall in the "don't need a label for this bond as it is simply based on respect and trust" :-)
But that being said, I am open to the possibility of their relationship falling into any one of the above categories as the series progresses and depending on how many seasons we get.
And yes, I am even open to the idea that the writers might end giving them some romantic label too because judging from the Ben Daniel's quotes from the interview above, it sounds like the writers are spoiling him with regards to what's in store for his character's love life in season 2 :-)