Okay, I just want to clarify that I cannot speak for all lgbt people, these are just my personal thoughts on the matter. This is a very long answer, sorry.
No, but I think the question is flawed. I mean, love is flawed from the start, right? Not a single one of us is ever going to be able to achieve true Christ-like love in this life, because we're not perfect. So, you're asking about "in order for the love to be real," but what even is "real love"? There's no one way to quantify or evaluate that, which is the reason why the arguments surrounding this question are so cyclical and unusually unproductive. Because one person's definition of love is different from another person's, and we're all ultimately talking about something we feel. Are feeling love and loving someone the same thing? I'm not really sure, but for the sake of this answer I'm conflating them.
For one, I think the reaction of "I love gay people!" from Mormons and other religions that have policies like ours is usually, at its core, a defense against accusations of homophobia. It's the thought process of "but if I say I love you then I can't hate/fear you!" But idk, this is just kind of useless? I don't need everyone in the world to love me. But I would like it if every gay person in the world could hold their partner's hand in public without worrying about getting beaten up, or feeling like everyone is staring at them. I would like it if every Mormon could be counted on to vocally and actively defend us against hate crimes and fight discrimination against us. Unfortunately, that's very much not the case. What does your love do, I think is the point here. And I think that's what most lgbt people mean when they say, "No, you don't love us." It's a shorthand way of saying: the love you claim to feel isn't doing any of the things that love is supposed to do (comforting, supporting, helping, etc.), ergo it's not love and/or it is but it doesn't matter. It's worthless to us and you might as well not be claiming it, because the effect would be the same either way.
Just as an example of what I'm getting at, most abusers love their victims. But that love doesn't save their victims from them, and it doesn't make up for or erase the abuse. That love is not useful or comforting to the victim. Or consider parents who love their children but don't always do right by them. Love is not a cure-all fix for any of us. In the same way, someone's professed love for gay people, whether they truly feel it or not, does not excuse them from the rest of their actions and words toward those people, good or bad.
So yeah, this is a long way of saying that imo yes, you can love someone while thinking that being gay is sinful, because love is always imperfect, and for most of us feeling parental and familial love isn't exactly fully voluntary. But more importantly I think the question is flawed, because whether or not a nebulous personal feeling counts as "real love" in someone's book does not magically make their actions loving. And what is love if it is not backed by action? (I like a "love without works is dead" concept here--consider reading James 2:14-17 but replacing the word "faith" with "love." I think it holds up pretty well.) Yes, I think a parent can absolutely love, or feel love for, their gay child while kicking them out of the house, but that doesn't automatically mean it was the right thing to do, and that love isn't going to save them from judgement for that decision, nor will it save their child from the potentially devastating emotional harm. Love is often imperfect and conditional, and I don't find it helpful to act like this isn't the case. Maybe the question everyone is so concerned with should be less about whether or not straight people's feelings (of love) are validated and accepted without question, and more about what they're doing to help this marginalized and downtrodden group in our society?
And since I've already made this really long, I'm just gonna throw some scriptures in here to get a spiritual angle. Let's visit 1 Corinthians 13:4-5 "Charity suffereth long, and is kind; charity envieth not; charity vaunteth not itself, is not puffed up, doth not behave itself unseemly, seeketh not her own, is not easily provoked, thinketh no evil..." the chapter continues. My point here is that charity, being the pure love of Christ, is kind, vaunteth not itself, is not puffed up, and seeketh not her own (which sends you to the TG for "selfishness"). Vaunting is defined as "to boast about or praise (something), especially excessively." Real love, in the Christ-like sense, does not boast, and it is not proud. So maybe we should ask why so many straight members feel the need to be boastful about their supposedly sincere Christ-like love for all gay people, and why they treat this love like something they deserve a trophy for.
Lots of thoughts going on here, so hopefully there are some points for you to ponder and I wasn't too confusing.