My neighbor [80sF] hates me [24M] because she thinks I’m cheating on my roommate [25M], who I am not in a relationship with

So, this is a stupid situation.
My roommate and I have the same job, which involves constant travel for more than half of the year. During that time, we’re only ever at the apartment for like a week or so every couple of months. Shortly before we left for like eight months, an elderly woman moved in across the hall. We saw her during the brief times that we were home and she was super friendly. About two months ago we came home for good (meaning until the travel part of the year). The neighbor was nice for like two weeks and then things changed dramatically. She death glares at me whenever she sees me. She gives terse, one-word responses when I try to make conversation. She still likes my roommate though. When she sees us together she’ll very pointedly say “Hello, [Roommate’s name]†and ignore me. A few days after that behavior started, she saw my roommate out by himself and told him she thought he should know she’d seen me come back late with a girl and then saw that girl leave in the early morning. Mystery solved. She’s just an ultra-conservative old lady who disapproves of pre-marital sex and thinks my roommate does too. He had inadvertently avoided her ire by going over to other people’s places instead of taking them back to the apartment. I figured there was nothing I could do, short of taking a vow of celibacy, to make the Old Lady stop hating me for being a dirty sinner, so I've just been trying to ignore it.
Things got weirder after that. About a month into us being home, Old Lady starts trying to set Roommate up with random people. Like, she’ll catch him alone and start going on about how her godson’s nephew or whatever is single and would Roommate like to meet him? Roommate always politely declines. Curiously, she only does this when my roommate is by himself, never when he’s with me. Odd, but whatever. Yesterday, Roommate told me about another strange interaction with her. They were chatting and he mentioned that he was going out of town this week and she said, “Oh, you’re leaving [My Name] alone on Valentine’s day?â€. Roommate thought this was odd, but just said that he was sure I’d be fine. Old Lady presses as to what’s so important that he’s going away for, Roommate says it’s a family event, and she asked why I wouldn’t be going with him to a family event. Roommate is like “Um, why would he?†and she says she just figured since we lived together I would be included in that sort of thing, but that it’s “probably a good thing that he [Me] hasn’t been made part of the family yet, given his behaviorâ€. Roommate assumed this was just more of her disapproving of me having casual sex and quickly ended the conversation. When he told me this, I came to a new conclusion. She thinks we should be spending Valentine’s day together, assumed I would be attending family events with him, and started trying to set him up with people (but never in front of me) after she realized I had slept with a girl. She’s doesn’t hate me because I sleep with people, she hates me because she thinks I'm cheating on Roommate. That’s why she’s trying to set him up with people. It also explains why she mostly suggests dudes, which I hadn’t even questioned before.
How do I tactfully clear up a misunderstanding of this scale that has apparently been going on for nearly a year (the anger at has been less than two months, but she moved in nearly a year ago and has probably thought we were in a relationship the whole time)? I really don't want to keep getting the evil eye every time I see my neighbor. It always feels like I've disappointed my grandmother.
TL;DR: Elderly neighbor started hating me after I brought a girl around. I thought it was a religious thing, but it turns out she actually just thinks I'm cheating on my roommate, who I am not dating. How do I clear up this misunderstanding?


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