If you genuinely didn't know, then I think it depends on how you respond when someone tells you.
If your response is to feel mortified, to apologise profusely and to make real efforts afterwards to go away and properly educate yourself on the issues, then no, I wouldn't personally regard you as being racist.
If your response is to defend yourself, insist that you weren't being racist, refuse to take the feedback on board and/or just shrug it off without trying to educate yourself further on the subject, then I think that confirms that you are actually just racist.
ETA your remarks would still be racist whether you intended them to be or not. But whether those racist remarks would make you a fundamentally racist person would depend on your response imo.
Obviously, there would be certain comments which you simply wouldn't ever make if you weren't fundamentally racist, and ignorance would be no defence. But I think it would be possible for a person who isn't racist to use a racist term without necessarily realising the racist history or connotations of the term. In such circumstances, my judgment would depend very much on their response when they were made aware.