Boy, was this a complicated question for me. When I met my now-ex-boyfriend, he was almost a year clean/sober. I never felt comfortable drinking in front of him, and so I didn't.
I also asked him how he felt about it - me drinking wine or beer when I'm not with him, and when I am with him. He said it didn't bother him at all. He wouldn't want me to get drunk or anything, but he said he didn't care if I had a drink or two with him around.
I still didn't do it. I had wine a few times a week, and told him I did, but I still didn't do it around him. Then one evening, we were out to dinner, and I'd had a migraine all day, and Tylenol and water weren't doing anything. I asked him if it would be alright if I had some wine. He said of course.
It was still a few more months after that before I did it again. I had gotten overly worried and uptight about the relationship, and one stressful day, I had a glass of wine before I went to see him. I thought it might be easier to be easy-going when I saw him. I confessed to him that I had. He said, "That's fine." And then, "It's working. Maybe you should do that more often. You can even bring some wine with you, if you take it with you when you leave."
And I did. 2 or 3 times. Meanwhile, I'd made an appointment to see a therapist because I didn't want to be using alcohol if anxiety was a real problem for me.
Nevertheless, a week later (before the appointment actually arrived), he broke up with me.