Let's start with some education so that we’re all on the same page. Your menstrual cycle is divided into 2 phases:
Ovulation marks the switch from follicular into luteal. And your period - ie. first day of bleeding - marks day 1 of your menstrual cycle.
This is important to note because your gut reacts differently to these different fluctuations in hormones.
Let’s start from the beginning.
At the start of your period there is a drop in progesterone as you move out of the luteal phase.
There is also an increase in prostglandins. Prostaglandins are not hormones but have hormone-like effects. They are released during your period to stimulate your uterus to shed it’s lining.
They can also have a stimulating effect in the gut.
The combination of decreased progesterone + increase in prostaglandins can cause loose stool.
The effect seems to be heightened when the gut is already irritated or if you experience IBS or IBD.
So while this increase in loose stool at the beginning of your period is not necessarily abnormal; there is a good chance that fixing your gut can help to lessen the severity of the problem.
There doesn't seem to be much influence of the hormonal changes during the follicular phase on the gut.
During the luteal phase, so the second half of your cycle your progesterone levels rise dramatically.
Progesterone can be seen as a calming hormone.
It has the calming effect on the brain (ie. can help lessen anxiety), and it can also exert a calming effect in the gut to the extent that it decreases intestinal motility.
This slowed motility can result constipation, which in turn can cause bloating.
An increase in progesterone also explains why constipation is more common in pregnancy.
What I just talked about is likely only applicable to those not using hormonal contraceptives; ie. have a true period.
Most pills contain synthetic versions of estrogen + progesterone that are being released in steady doses throughout your cycle. You will not be getting the fluctuations in hormones that you get with a true menstrual cycle. This means that you likely aren't getting a change in gut symptoms over the 28 day period.
But, hormonal contraceptives can have other effects on the gut - mainly by altering the gut microbiome (decreasing the beneficial bugs). And this can cause inflammation, which can cause symptoms like changes in bowel movements and bloating.
Poor gut health can lead to higher levels of estrogen in the body.
When you have too much estrogen circulating in the body you can end up with what is termed estrogen dominance.
Estrogen dominance can lead to painful & heavy periods; and more PMS symptoms.
So hopefully you can see that regulating your hormones is important for the state of your gut and that the state of your gut is also important for regulating your hormones & your period.