Can One Be a Christian if Jesus Didn't Rise Not really philosophy more text-specific analysis, but if it's permitted.
Generally, a person can identify as whatever they please. Certainly schools of thought, ways of life, and religions hold doctrines that one must adhere to or accept to be considered a true follower or not "hypocritical." "Problem", per se, is that, like most things, different people agree and disagree on different things, hence, in this case, why certain religions have unique denominations, often a result of what was- in many cases, at first- a small splinter group or movement. Christianity is no exception. Protestants believe one thing, Baptists believe another, Catholics, another still- to the point others have stark disagreements where one views the other as "simply wrong". I believe a few "popular" disagreements are works-based salvation vs. faith-based salvation, per-tribulation Rapture vs. post, etc. One who believes one thing and not the other generally views the other person as "lost" or, again, "just wrong" or even not a true whatever the title or group happens to be.
Whether or not Christ was raised from the dead (physically, hence the purported visual apparition allegedly witnessed by followers) seems to me like an incredibly minor detail based on the underlying context of Abrahamic faith (which again different followers hold different beliefs as far as what the purported Messiah is, signifies, and functionally "does") If I'm not mistaken, Jewish prophecy states the Messiah would be a military leader who would ensure them a victory against their enemies. Christianity states Messiah (literally messenger), as exactly that, a messenger who gave men a heavenly decree that the Old Testament is no more, and those who follow the god of Abraham have new (more lax) laws to follow, as well as, well, to put it casually, something of an "update" that mortals are now allowed in Heaven provided they meet certain conditions. This, if I'm not mistaken, is a change from the way it was before as Heaven was previously reserved only for angels and divine beings (and possibly those who God "likes", I guess, not sure- but based on the doctrines of the faith an all-powerful god can in fact do anything, so, yeah.) If I'm also not mistaken, Jews generally believe Jesus was not the prophecized Messiah and was either A.) a liar and/or B.) just some guy trying to make everyone feel better. Which means they await the true Messiah who, as they believe, has yet to come.
To your point, you are a Christian if you believe in Christianity, the idea Jesus existed and, presumably, was the son of God, and/or by extension (though again depending on belief the two are not mutually-exclusive), the foretold king/prophecized Messiah foretold in Jewish texts. You could be a "bad" or "untrue" or "lost" Christian, I suppose, why not? To answer your question one asks the opposite: what is a non-Christian? Typical answer being someone who "doesn't believe in the Bible" or that Jesus existed and performed all or most of the purported doings and activities alleged, whose word is the Truth, believes such, and strives to live as Christ (rather, God via Christ) commanded or stated one should. (You can believe in all of the above, but reject the idea, and live in willful opposition to the alleged new ("Christ's") commandments, that would make one a non-Christian).
Basically, Jews and Christians ultimately believe in the same Messiah, one just believes the other is wrong. Christians believing the ancient scripture was fulfilled and as a result anything commanded or proclaimed by Jesus is divine and eternal law, Jews believing said prophecy has yet to be fulfilled and nothing has changed from when God purportedly gave Moses the Ten Commandments to before the day Jesus was born to now (and naturally as a result Christians are misled, at worst damning themselves and those around them or at best wasting their time). Kind of the same as what they believe of them.
To put it casually: was it the real slim shady or not? Therein lies the only divide between Judaism and Christianity.
Personally, I believe in a compassionate, all-knowing God. Which means God obviously knows that people are pretty dumb. If you're a good person, and there's a Heaven mortals are allowed to reside in, you'll probably end up there. If not, mankind is pretty boned any way you slice it.
(The reason I call this non-philosophy is because the ultimate goal of your question is a result of what a purported text or school of thought ultimately resolves to. It's an explicit yes or no, 1 or 0 binary based on explicit, static information [whether the information is true or false is not the issue] and nothing more. Meaning, logically, the answer remains the same whether or not you are a devout Christian or an atheist who views this as a discussion on par with what Santa Claus' favorite cookie is.)