I'm an atheist who believes in much (not all) of the teachings of Jesus. Are there other Atheist/philosophers who discuss the teachings of Jesus from an atheistic perspective?
Being a cultural but not religious/theological adherent is far more common in Judaism, & increasingly Islam. There are reasons for that, not least that apostasy in Christian countries has not been a problematic matter since the widespread adoption of secular governance following the European wars of religion. There are almost infinite flavours of Christianity to choose from, and more than that of influenced philosophies. In Judaism and Islam there are cultural sacraments, above and beyond the epistemologies - Durkheim is great on this, the power of festivals over catechisms to bind communities.
Jordan Peterson describes the 'Judeo-Christian substrate' as the non-theistic impacts of Christian thought. It is a highly controversial and suspect framing that lends itself to racism and cultural imperialism. Beware of that.
Christianity was profoundly influenced by Hellenic ideas, and especially the philosophy of Plato. Boethius' book 'On The Consolations of Philosophy' drew on Greek thought including the Stoics, to address Christian questions, and had a huge influence on European thought. In many ways Christianity is Hellenic thought filtered through the lens of monotheism, rather than a branch of Judaism - see for instance the origin of Hell & the Devil, as well as the suspicion the Trinity is held in by Judaism at large. You could say Humanism and its more active recovery of Classical thought is a truer follower of Christian tradition than the Puritans.
What Jesus is recorded as saying is far from a coherent philosophy. It was pretty minimal: general platitudes & the Golden Rule. The pope gave a response saying following the words of Jesus alone is not enough to be Christian, though I've not located the statement.
Personally I am fascinated by the Gospel of Mary, which chimes far more than what St Paul said with what Jesus actually said. I really like 'Jesus the Man: New Interpretations from the Dead Sea Scrolls' by Barbara Thiering, as a way to grapple with text inconsistencies especially about geography and journey times, and to reconcile with the earliest biblical texts and what we know of the Essenes. Even being willing to listen to these ideas could have got you murdered in most of Christendom for the majority of two millennia. Doubting the literal truth of transubstantiation was a big part of the Protestant split from Catholicism, and centuries of war. Drawing culturally or philosophically from Christianity, it's important to understand religious adherents may consider you less of an ally than they would a pure atheist - especially if you challenge their ideas in detail from genuine curiosity about texts and history.
I see Ecclesiastes as part of the true Wisdom Tradition literature; a profoundly rebellious text that crept into the core canon in defiance of the verities of the powerful, and worth close scrutiny by anyone. I'm a lot more interested in what Rabbinic scholarship has to say on Jewish thought than what largely ill-informed Scholastic philosophy says on it.
Don't believe it. Read it. Draw on it. Be inspired by it. Come to know it, in your own life. Far better than any statement of faith.