That "Gemini curse" is of her own making. If she was interested in you romantically at first, she's obviously not incapable of being more than friends with anyone born in the last week and a half of May or first three weeks of June. That she "can't be more than friends" with Geminis is her own personal decision to consider certain birthdates a deal breaker.
She must be basing that assumption on sun sign astrology, which is half baked at best. Sun sign astrology equates your sun sign with you. Real astrology acknowledges that we all have all the signs in us. Sun sign is one of the signs that's highlighted--your sun sign represents the kind of personal growth you need over your lifetime--but any other sign where you have planets, or the moon, or your ascendant, is also highlighted. Signs are archetypes that we all carry within us. Highlighted signs, including the sun's sign, are the archetypes we express the most and respond to the most.
The next bit of information your "lady friend" has apparently garbled is aspects. Simply put, aspects are geometric angles between planets, and they depend on sign placements. Some aspects are considered harmonious, while others are considered challenging. It might be summed up as saying the planets "get along" or "don't get along." Gemini and Virgo are 90 degrees apart, so if planets in them form an aspect, it's a square, which is one of the challenging aspects. Hence the myth that Geminis and Virgos are incompatible. The truth is much more complex.
Gemini and Virgo are archetypes that act in very different ways and "want" different things. In that respect, they're at odds. But that being at odds doesn't play out between people with those sun signs so much as between the Gemini and Virgo in an individual birth chart.
If your birth chart has a planet in Gemini and a planet in Virgo (for astrology purposes, the sun and moon are also planets), and they're within 5-10 degrees of forming a 90 degree angle, that's a square. That means the parts of your own psyche represented by those planets "want" very different things. You might experience that as a battle within yourself, between competing desires. You might try to quash one of those desires in favor of the other. You might get stuck between those competing desires and not be able to do anything. Or, if you respond in a healthy way, you might find both of those desires sharpened and strengthened, each in their own different way.
If your sun and your friend's sun form a square, all that means is that your core personalities want very different things and need to grow in very different ways. That doesn't make you incompatible with each other. It's certainly possible for couples to both be developing their personalities in very different ways, while supporting each other's growth and harmoniously sharing other parts of their lives.
If your birthday is May 30th and hers is September 15th, your suns are square by sign, but they don't form an actual square because the orb (distance between them) is too wide. May 30th is early Gemini and September 15th is late Virgo. Those dates would put your suns about 20 degrees away from a 90 degree angle. That would serve to lessen the friction. However, you could have a perfect square between your suns and still be a good couple (if not for her decision not to consider Geminis!) because in that case, the square might be what provides the spark to keep the relationship alive, especially if you have lots of harmonious aspects in other parts of your charts.
I have a prime example of that in my own family: my parents. Mom's an Aries, Dad's a Cancer--square by sign--and they both have their suns in the same degree of their signs, so their suns form a perfect square. They've been pretty harmoniously married for 43 years and counting. I did realize, though, after taking up astrology, that my parents do have very different personalities from each other--rather a shock for a daughter who always thought of them as a unit, just mom-and-dad!--and yes, they pursue very different interests day to day, and always have. But they also have a few shared interests, which is how they spend time together, and they get along well when it comes to living together. So, in their case, the sun square is probably the spark that keeps the marriage alive.
