No, if you're homeschooled, you don't lose your social life. But, I did... and that's only because I had 3 friends in the first place. D: They either moved or their parents started hating me, so not my fault, huh?
Homeschooling is actually a good thing. No, you don't have to stick to a religion. [I didn't even go to church when I started homeschooling. Many curriculums, though, ARE religion oriented.] No, you don't lose your social life. No, you won't become a nerd. But, it actually helps your grades and schooling. I was public schooled until 7th grade, then my parents pulled me right out and I'm so incredibly glad that they did. I now have a perfect average, I get all As and some Bs, and before I mainly got mixed As and Bs in public school because no one was helping me learn any of the stuff, mainly math. I was on my own for most of the stuff, and it was very frustrating when a teacher expected you to learn something just like that. And it was also annoying when we skipped around in the book and didn't finish it... >__<
You also get to take any classes you want. Want to learn French, Japanese, Latin, etc.? I'm learning Japanese right now, and I probably would've been stuck with a language I hate in public school. I also get to count artwork as school work, so I can paint, make clay items, draw, work in Photoshop, and it's plenty more fun than the art classes I did because you get to do what you want.
With public schools, they don't really help you with things you have problems with. Each teacher has their own class to deal with, so helping with specific things for specific students is hard. But, with homeschooling, you've got plenty of people to help you understand concepts. Your parents, teachers from a curriculum [I'm on one of those curriculum things. You send tests in, they grade them, and you get them back. There's self tests, too, but the answers are in the back of the book, and you don't send those in.], parents on any 'email' groups for homeschooling, and even the book itself sometimes. What's also good about homeschooling is you go at your own pace, and you actually finish the material, unlike what happens at some public schools.
If you're worried about losing your social life because your parents want you to succeed, don't be! There's plenty of ways to make friends and say in contact with your friends. You can meet new people at tons of places, and you can keep in contact with your friends VIA email, phone, IM, actually meeting them, whatever. I kept in contact with my best friend, and we hung out a lot over the summer when I first started homeschooling. It's not that hard.