This question is difficult to answer succinctly because the more desirable wording to use may differ depending on the circumstances surrounding the statement.
Case 1: When Maybonne was your girlfriend, she often ate at Red Lobster. Now that she is your ex-girlfriend, she may or may not eat there. If you know that she still does, it makes sense to say "My ex-girlfriend eats at Red Lobster." If you don't know whether she still does, or if you know for a fact that she doesn't anymore, the more accurate statement would be "My ex-girlfriend used to eat at Red Lobster"—the implication being "When she was my girlfriend, she used to eat there." A stickler might insist that saying she used to do something implies that she doesn't anymore, but few English speakers insist on drawing that logical inference when dealing with a written statement, and even fewer insist on drawing it when dealing with extemporaneous speech.
Case 2: If, when Maybonne was your girlfriend, she was into karate, and that's what you're trying to say, "My ex-girlfriend used to be into karate" is a reasonable way to say it. It's true, again, that some hearers may infer from that wording that she is no longer into karate now that she isn't your girlfriend—but it is equally true that hearers might infer that the statement "My ex-girlfriend is into karate" indicates that karate is a hobby she took up only in her post-you career. In real life, a sophisticated English speaker might recognize and avoid possible misunderstanding on this point by expressing the idea along the lines of "After we broke up, my ex-girlfriend took up karate, and she's really into it now." But not everyone is so clear.
Case 3: If Maybonne is tall, obviously her status as a girlfriend or an ex-girlfriend doesn't alter that fact, any more than it alters the fact that she is from Missouri (let's say). But in this case, use of the past tense produces an odd effect. By identifying her as your ex-girlfriend, you assign her a current status: she is, right now, your ex-girlfriend, and her height and state of origin are, as KWinkler observes in a comment above, permanent attributes. So there is something slightly morbid about saying, "My ex-girlfriend was tall, and she was from Missouri." But no such sense attaches to the seemingly very similar statement, "My first girlfriend was tall, and she was from Missouri." That's because "first girlfriend was" puts Maybonne's status in the past and indeed may be necessary to avoid suggesting that your first girlfriend and your current girlfriend are one and the same person. If you say "My first girlfriend is tall, and she is from Missouri," the implication is that your current girlfriend is your first girlfriend—though the wisdom of referring to her in this manner is perhaps as dubious as referring to your current wife as "my first wife" when she is the only wife you've had.
Whether to use past tense or present tense in describing the activities and characteristics of a person you've identified as your ex-girlfriend depends on the rather subtle distinction between whether you mean "my ex-girlfriend today" or "my ex-girlfriend, back when she was my girlfriend." People tend to express themselves more loosely on this point than a strictly logical person might wish them to, but fortunately you're not operating in a vacuum: clues from nearby sentences should provide hearers or readers with the necessary context to understand your intended meaning.