I am neither a doctor nor a chemist.
The following statements rely heavily on the German Wikipedia article on chlorogenic acid and some other sources that are typically considered trustworthy (e.g. PubChem and others citing studies.
Individual reactions may vary.
So we have two suspects that may or may not be responsible for stimulating your digestive system.
Chlorogenic acid sounds like a good candidate for stomach issues (being an acid), but in animal testings it actually helped against ulcers and there are no indicators of other plants containing chlorogenic acid causing problems.
High contents in coffee can be tasted and the content is significantly influenced by the roasting method, slow roasting at temperatures around 200C will break it down, which will additionally make the coffee taste milder. I suspect that the perceived flavor contributes to the ascribed properties that are sometimes mentioned on more popular (non-scientific) websites. But I assume that it’s not the chlorogenic acid per se, but the general roasting method and bean quality that matters here.
Caffeine on the other hand is a proven stimulant, which affects the nervous system - including the peristaltic movement of the colon, causing the known effect of urgent bathroom trips up to diarrhea. It’s also an - albeit weak - diuretic, resulting in frequent urination. The symptoms you describe in your question are classic caffeine effects. If you are suffering, the dose is too high for you to stomach (pun intended). You can develop a tolerance (we have some Q/As on the topic here on the site), but reducing the dose or skipping the caffeine is the logical way of avoiding the effects.
So my conclusion:
If you want a “mostly harmless” drink, go for decaf and don’t worry too much about chlorogenic acid. If you want a mild coffee and are ok with the caffeine effects, go for slow-roasted - which I would generally recommend.
Finding a coffee with both properties may be a good reason to get familiar with your local roaster instead of buying at the supermarket.