In the past it was unusual for a home schooled student to attend a highly selective college in part because the colleges didn’t know what to do with a student with no grades other than those give by one of their parents.
While some colleges still are wary about home school students, the number of colleges welcoming these students is increasing every year. What the colleges have finally figured out is that strong, talented students come from a variety of backgrounds including some who are home schooled. It is true that home schooled students need to show some basis for their academic strength outside of their grades. But keep in mind that while grades are the most important factor for most colleges in admitting a student, it is not the only factor. Test scores, essays, and recommendations are also important and even more so for students without traditional grades. Home schooled students, and their parents, do need to keep in mind that all colleges, and particularly selective colleges, like to see students who have a strong background in all five academic subjects including English, math, social studies, science and foreign languages
Recommendations can sometimes be a problem for home schooled students since colleges generally do not like to see recommendations from parents. In the alternative, many colleges will accept recommendations from adults who know the student well. This can vary from college to college and home schooled students will need to make sure that they understand what the colleges want as part of their application.
Getting an interview can also be important for home schooled students. An interview, whether with an admissions officer or alumni interview, allows the student to communicate their academic strengths as well as explain how that student can contribute to college life.
Finally, if a home schooled student has the opportunity to take college courses while in high school that can significantly help the student to prove that they are capable of handling the work at a selective college.
The National Association for College Admission Counseling has a webpage that provides additional comments on what the home schooled student needs to consider for college admissions.
If you are home schooled you can still consider selective colleges as long as you do your homework on the colleges you are considering. You just need to show why you are a student that will provide something of benefit to the colleges you are looking to attend. Which is exactly the same thing that traditional students need to show.