Does it have an effect? Probably. Does it have as much of an effect as some people would have you believe? No, probably not.
Humans are sexual creatures. We are biologically compelled to have sex (well, most of us anyway). That's sort of the reason why we have an overpopulation problem. Rihanna isn't making sex more popular. Her music is popular because sex is popular. Her music is a symptom, not a cause.
Having said that, there is a negative impact to her music: it makes people more animalistic, impulsive, and sex focused.
I am very well aware that humans are animals, and that we have an animalistic nature and instincts. I am also of the mind that these instincts do not serve us well in the future. Unlike other animals, humans have a sufficiently developed intellect. We can create societies, we can modify our environment, and most critically of all, we can REFLECT on our actions and our instincts. We are self-aware to a degree that no other animal is, because we can actually question our nature and our desires and our instincts and change them radically.
Our instincts were vital for our survival on the savannah. They are less vital now, and in some ways they are actively harmful. The desire to have sex all the time, or to focus on sex exclusively, or to hold it up as a vital part of life, is harmful to human society - which is overburdened with too many people. Having a lot of sex and having a lot of kids as early as possible was an evolutionarily beneficial tactic in the days where the average life-expectancy was around 30 and most infants died before their second birthday. In this day and age, where children are expected to grow up in a stable household, and the infant mortality rate has plummeted, this sex obsession instinct is actively harmful to our long term interests.
Rihanna's music - hell, most pop music these days, and certainly almost all rap music, encourages emotional thinking, rather than rational thinking. It encourages the mindset of "IF IT FEELS GOOD, DO IT" (which I am aware was created in the 1960s, but the spirit of that saying is alive and well in this day and age). It encourages you to follow your heart, not your head. It values emotions over logic. It values outbursts over discussion, action rather than contemplation - it screams "GIVE IN! GIVE IN! GIVE IN to your basest desires! Don't think! Just feel! You wanna have sex! YEAH! Get it on! BOOBS! PENISES! SHOW SKIN!" The after-effects of such a "philosophy" (if it can be called that. You know, 200 years from now, people will still be talking about John Locke and Kant. Those were real philosophies. No one in 200 years will be talking about Rihanna, because her stuff is intellectually worthless. Come on. You know it is) are rarely explored in her "buttocks gyrating" "Music" videos.
These music videos encourage a culture of: "You find them hot!? DO IT IN A BATHROOM!". It advocates that women and men should follow their carnal desires without regard to well being, the future, STDs, potential pregnancy or emotional well being. It encourages animalistic humping rather than sober, careful reflection.
You see this all the time in modern music and pop culture. From Elvis to the Rolling Stones to Rihanna or Snoop Dog or whatever it is kids like these days.
Of course, Rock'n'Roll and Rap Music won't destroy society. That was where the "Cultural" conservatives were wrong. But it does encourage young people to act out, to go wild, to do it if they feel they want do. Of course, you can argue (correctly, in my opinion) that teenagers have been acting out throughout all of human history. But at least they'd have the good sense to be ashamed of it in the past. These days, buck wild, immature, selfish desires are celebrated by Western society. Scholastic endeavours? Scorned. Intellectual pursuits? Ignored. Sober, contemplative reflection on your own behaviour? Apparently that's just for squares. The idea that one should RESTRAIN their emotions, think carefully about problems, consider the consequences of their actions.... that's lost on today's youth.
No, I am not a religious fusspot. I'm an atheist. No I'm not an old bitter man. I'm only in my early twenties. No, I'm not some white guy railing on about the "destruction" of my culture (I'm only half-white, and I've lived in many cultures and nations throughout my whole life). But I am a sensible, careful, reflective person. I value stoicism and an apollonian nature. I see the youths of today act like feral cretins. Screaming, shouting, jumping up and down like little animals. I see them abandoning mathematics and science in droves (no wonder half the members of the labs I've worked in are Chinese or Indian, because those societies still value intellectual endeavours). I see a society that developed the technology to travel to the moon, turn its attention to grown men swiping credit cards through the buttocks of a stripper on TV. And I am disgusted.
Do the young people of today really see no worth in intellectualism? In restraining one's emotion? Of suppressing one's desires? Of thinking of tomorrow rather than today? Don't they realize that the pleasures of the flesh, while nice, are petty, passing and infinitely more shallow than the pleasures of the mind, of thought, of calm contemplation?