[quote="mariahloves, post:1, topic:196007"]
I have recently become interested in Buddhism as a philosophy.
There's much to be interested in.
While I am a Catholic, believe in God (the Father, Son, and Holy Spirit), the Bible, and sacred tradition, I also find myself sharing some common beliefs with Buddhists.
There's a big step from saying that you share "some" common beliefs with Buddhists (there are few people on the surface of the earth with whom I don't share some common beliefs) to expressing a desire to call yourself a "Catholic Buddhist."
I don't consider Buddhism a religion although it's usually classified as one. There are no God(s) or Goddess(es) in Buddhism.
First of all, that's not quite true. In traditional Buddhist cosmology, there certainly are gods and goddesses, but they cannot bring salvation, and thus their worship is not a part of the Buddhist dharma properly speaking (though Buddhists may pay homage to various gods and spirits for purposes unrelated to final enlightenment, as I understand it). Furthermore, in Mahayana (and Vajyrayana) Buddhism one could argue that the buddhas and boddhisattvas are essentially gods and goddesses. Certainly the line between the two categories often seems quite thin, as when some Japanese Buddhists identify the Shinto kami Amaterasu with the Buddha Vairocana.
More to the point, why define a "religion" purely in terms of "gods and goddesses"?
There are certainly many devotional practices in Buddhism that look like what we normally call religion. The problem is that "religion" is hard to define, and some scholars (most recently and notably a scholar of Japanese culture, which may be relevant for the present discussion) have suggested that we should just stop using the term at all. But if we are going to use it, we should probably use it in a broad rather than a narrow sense, and should certainly not base theological arguments on our own rather arbitrary definition of "religion."
The same goes the other way: conservative Christians can't just say "obviously Buddha is an idol because he's a figure in a non-Christian religion." Both sides need to define just what in Buddhist belief and practice is compatible or incompatible with Christianity. I'd like to hear that argument from you--your OP is rather vague.
I was wondering if I could be a Catholic-Buddhist without going against Catholic teaching. Any thoughts?
To quote Pitti-Sing from the Mikado, "Bless you, it all depends."
You really haven't explained just what you mean by a "Catholic Buddhist," so how is anyone to answer your question? (This hasn't stopped plenty of people from trying, of course.)
Which school of Buddhist philosophy do you have in mind? Generally, the Buddhist doctrine of "no-self" is considered rather hard to reconcile with the Christian doctrine of God and of humans as made in God's image, but I've heard attempts to do this based on a radically apophatic doctrine of God.
I would recommend the Buddhist section of Paul Griffiths' Christianity through Non-Christian Eyes for some thoughtful Buddhist perspectives on this subject (and Griffiths' introductions are helpful for a Christian perspective--Griffiths is himself a Catholic theologian and an expert on Buddhism). I find the pieces by Dharmasiri (a critique of the Christian doctrine of God from the Theravada perspective) and Masao Abe (a constructive and appreciative evaluation of the differences between Zen and Christianity and what each can learn from the other) to be particularly helpful.