This is indeed an important topic, and can be approached from different angles. One necessary point to mention is the difference of methodology of scrutinising narrations between the Usuli Shia scholars and the Akhbari Shia scholars. The would determine the form of how this question is answered. Of course, if we discuss this here it would become a very long reply, so I will keep the answer brief.
The narrations that point to Imam Hasan al-Mujtaba (a.s.) being a mizwāj or a mitlāq, which means someone who excessively marries (zawāj) and excessively gets divorced (talāq) is completely refuted and rejected by all our Usuli scholars, and for Akhbari scholars, they interpret it in a certain way, or withhold their opinion.
Indeed, the presnce of these fabircated narrations is was just another scheme played out by the evil Abbasid propaganda against Ahlul Bayt (a.s.).
Some of the number of ex-wives that have been mentioned are way beyond any rational acceptance, like 300, or even more.
Numerous Shia historians have discussed this, and refuted it all. Yes, there are mentioning of the Imam (a.s.) having up to 20 wives (taking the maximum number mentioned), but not all at once. This was something very common and normal at that time. We can also not verify exactly if this was the case, and whether some of the wives had more than one name, which meant that she was counted as being more than one, but in reality it was one person.
Please read this interesting article on this topic:
With prayers for your success.