I think it's important to distinguish between the idea of inevitable outcomes based on the principle of cause-and-effect (e.g. if I drop a glass it will fall, if it falls it will break, if it breaks and I step on it with bare feet I'll cut myself) and fate based on the belief in some kind of divine party that's interested in the course of a human life (e.g. Margaret is fated to marry, but her sister Diana is not).
The former is a fundamental principle that orders the universe as we understand it, and I think it's impossible not to believe in it. After all, no one on earth has ever dropped a glass and not had it fall. However, this idea of causal predetermination of certain events really is impersonal. It doesn't have anything to do with any individual, and it's just a set of laws within which we must operate.
The latter idea is harder for me to swallow, because it generally relies on the belief that the agent shaping fate is actively interested in one individual's life and well-being. It's personalized and personified, so that some interested party orchestrated events for Margaret to meet her future spouse on a street corner but chose to keep Diana away from any marriage prospects. The idea that any supernatural agency could actually take that much interest in a human life--especially when there are far larger issues to take care of on a global scale--is difficult for me to accept.
Of course, a third definition of "fate" might be simple luck: events that affect our lives that are beyond our control. And of course these do occur and they do shape our development in ways that we can't predict. But there's no evidence--or at least none that I have been presented with--to move from luck to predestination. Sometimes things happen at random, for good or for ill, but I don't think it's necessary to move from that to a divine roadmap charting out events in a person's life.
Regarding the use of these conceptions of fate in Tarot, I'll use the first but not the second or third. I can look at the principle of cause and effect, because it's something that I as a reader can analyze (e.g. if you return to the man who's cheated on you twice before, you're likely going to get hurt). But as for the second, I've been given no reason to believe that some kind of (benevolent) capital-F Fate is at work, let alone that I can somehow read that Fate's will by looking at a bunch of cards with pretty pictures drawn on them. And for the third definition, well, the whole point of unpredictable events is that they're unpredictable; I don't have the power to read them beforehand, only to interpret their effect after the fact.
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