Know What you're getting yourself into.
Starting on that site I was 11, and now it's been a good decade and I've quit, I was a growing creator. Now let me tell you before you go and jump the gun, when anyone who hasn't been on the site (for the right reasons), will assume IMVU is associated with sexual themes. If you can control yourself and go into GA (general Audience) rooms and take care of yourself, not sharing personal information and just chatting with strangers, then that's completely fine. There are apporpriate rooms you can look for... for example I like gaming and anime, I'll search in the bar "anime, chill, games" and you will get rooms that show up with those tags, meaning their intentions as well.
Were you to search "sexy, hot, naked" then you're trying to look for trouble. I can say that most times when you've decided to randomly enroll yourself in a "instant" chat, and you get paired up with a creep asking ASL (Age/Sex/Location). By any means you are NOT required to answer this person, you can avoid putting yourself into those unwanted situations were you to just leave, find another room.
Although it is filled with idiots, goons and fiends.. Like really all you need is common sense and morals. If you respect yourself enough you wouldn't go into a chatroom that would be 18+
As many others have said before in order for anyone to see AP (access pass) anything, this entails PVC, thongs, cleavage, nudity, sexual themes, nipples etc, then you pay a once in a life time price of $20 for the AP. Then when you see rooms were you to own an AP, you would see the letters on the chat picture. This means you are putting yourself into a room and situation where you know people could be wearing sexy things and talking about stuff of the sort.
I as being a creator I had my own personal fun by making my own rooms, buying furniture and making my own space, it was like my thing. So again before you bash on it, you should teach your kids not to be so gullible.
So you may not like the avatars, well the truth behind that is, some people dunno how to dress their avies, some people do. You may not like someone cussing.
If you spot anything inappropriate and it doesn't fit the rules of the room you are in then you are more than welcomed to report the persons at fault. But if you have real trust issues with your kids, you can stoop so low and put a keylogger in. That way you will see where they go and what they type, and if you see that your child is lying through their teeth, and are putting themselves in potential danger and exposure to sexual themes... then by all means have everything in your power to disable that app.
**You should blacklist it from your firewall/anti-virus, so they can't access it**