Christians can enter temples. There's a difference between visiting and worshipping there. I've entered Buddhist and Hindu temples, Jewish synagogues and even Muslim mosques before. However, for synagogues and mosques, it's customary to be escorted by a Jewish or Muslim friend and the prayer halls are for believers only, out of bounds to non-believing visitors.
There's no problem with walk-in entry to any Buddhist or Hindu temple. But it's respectful to dress, behave and speak appropriately. I've even attended a Buddhist course in a temple for a few months. They have no problem with me putting "Christian" on the application form and "non-religious philosophical interest" as the purpose of attending the course.
In fact, I agree with most of Buddha's teachings about humanities. Nothing much clashes with Jesus' teachings except the doctrine of reincarnation, which wasn't even Buddhist to begin with; it was Hindu in origin. And of course, Buddha had never claimed himself to be God. I looked to him like a great teacher and philosophy. Just like ancient China's Lao Tze taught nature and universal balance, but somehow his Taoism became a pantheon of deities.