Freedom of Religion

[Abracadabra]

Would a similar definition for "buddhist" be equally as shaky?

Oh absolutely. Buddhism has so many different philosophies it wouldn't even work to define a Buddhist as one who follows the teaching of Buddha.

Which Buddha?

Some people aren't even aware that there are many different Buddhas in the various forms of Buddhism. There are actually hundreds of different Buddhas.

Siddhartha Gautama is without a doubt the most famous, and often the one who is cited for having popularized the religion. But there are many others.

In fact, Christians might be interested in Amida Buddha since Amida Buddha is much like Jesus. The Amida Buddha offers salvation as pure grace. All you need to do is accept the gift of everlasting life offered by Amida Buddha and he will accept you into his kingdom of everlasting paradise. Not unlike the concept of the grace that Jesus supposedly offers along with acceptance into his heavenly kingdom.

However before you get too excited about this, I might add that this form of Buddhism was actually created by Buddhists who had been exposed to Christianity. So it's obviously a copy-cat religion, IMHO.