Yes, since the 80s they teach foreigners. One thing you should keep in mind is that it is not possible for foreign inductees to become a complete Shaolin monk. This position is reserved for Chinese citizens only. It is not a question of racism but a question of legal status within China that prevents foreigners from taking rank in the temple.
The monastery constantly accepts foreigners as students. However, foreigners cannot become real Shaolin monks. You can train as a disciple under the guidance of a true monk, but you will never be able to live in the monastery, nor will you receive the same training and experience. A commonly heard myth regarding the Shaolin temple is that only men can train there.
While it is true that all warrior monks who teach in the temple are men, both men and women are welcome to come and study there. As the center of Buddhist culture and the birthplace of Zen Buddhism, the Shaolin Temple is dedicated to being an open environment, welcoming all who wish to learn and experience what it has to offer. It usually takes a foreigner about 10 years from entering the monastery to the point where he is considered skilled enough to be a “warrior monk”. But the teaching method at Shaolin Temple means that everyone can at least have an idea of what it means to train traditional kung fu, and perhaps even open the door to future training, if people so desire.
Shaolin Temple has outreach programs that try to spread its message and training to new groups of people. I also knew that this was a business and that the Chinese government had its hands on the cookie jar of the Shaolin franchise. Shaolin kung fu practitioners, Shaolin monks, are also regarded as some of the most committed warriors. There are also some “short training sessions” available in China, which do cost money to attend, in which someone may choose to do some of Shaolin's workouts without working to the end to master them.
The original fighting style taught at Shaolin Temple seems to be “the 18 Luohan methods that form the basis for the development of the unique styles of kung fu taught today. The reason why the Shaolin Temple was founded was to allow Chinese monasteries to better protect themselves. Most people choose to study Kung Fu in Shaolin because they want to receive the most authentic form of training. Thought to have been founded in the 5th century AD, the Shaolin Temple is the main temple of the Shaolin Buddhist school to this day.
Foreign students studying abroad at Shaolin Temple generally do not go through the hard training that the temple's resident monks endure. When someone reaches the level of warrior monk, he is good enough to fight for the Shaolin and participate in demonstrations of his athletics representing the temple, and he is also good enough to found his own dojo and teach within it. In the Shaolin Temple of Songshan in Dengfeng, Henan, monks usually take care of foreigners for training. After kung fu movies like Jet Li Shaolin Temple made the site famous abroad, wide-eyed foreigners like me made it their mission to train there (you'll notice in my bio below, that's why I started learning Mandarin in the first place).