I've yet to find any koan or other forms of Buddhist texts explicitly mentioning Ji Gong, so it's difficult to say whether he was 'accepted' by some schools or not. But we can look at other factors.
Are there precedents? Yes. There are many well-known (and greatly revered) bizarre monks in the history of Buddhism. A notable example is Drukpa Kunley, who allegedly used his penis to subdue evil and had had sex with thousands of women. More on par with Ji Gong would be Hanshan (寒山) and Shide (拾得), who are often depicted with distinctive expressions, heads full of hair and wearing ragged clothing. This duo are pretty popular in Zen, and, similar to Ji Gong, are believed to be the incarnations of Manjusri (文殊) and Samantabhadra (普賢), despite behaving like lunatics.
Should monks behave like so? Hard to answer. Monks keep the precepts to cultivate compassion and develop the mind. But one can argue that, since an enlightened being is unattached, unbound and know what they are doing, they need not to follow the precepts as long as their actions help others grow spiritually and reduce their suffering. Although there are differences between the craziness of an enlightened being and that of someone with mental illnesses (see Andrei's answer on crazy wisdom), there are times where the distinction can be blurry.
Note that this line of thinking only applies in one direction. It does not justify doing scummy things and then later claiming that you've done so because you're enlightened.
To sum it up, these monks - Ji Gong included - presumably knew what they were doing. The benefits of the monastic rules are not negated by their acts. If you're a beginner, it's still best to keep all the precepts.
There are already many answers concerning fortune telling:
AFAIK, those who provide and engage in fortune telling in Buddhist temples in China are not monastics, so the Brahmajala Sutra won't apply to them (a.k.a not wrong livelihood). My take is that if you aren't obsessively into fortune telling, the practice is harmless.