As I understand it, the 'not before 12 weeks / in the first trimester' is to cover the teacher in case of miscarriage. But not because there's any sense that yoga or any other activity would cause a miscarriage.
To give you an example, I've had a miscarriage. Was an ivf pregnancy so closely monitored and I knew the embryo had stopped developing at around 6 weeks, confirmed by a blood test. I stopped taking the drugs which support the pregnancy (extra progesterone). But for a few days nothing happened. No bleed. I then went and did a fairly dynamic yoga class and the bleed started with gusto as I left the class.
I KNOW that class didn't cause the miscarriage, the pregnancy was over days before and that had been confirmed by a doctor. But if it's been a less supervised pregnancy and I'd not know all that, it would have been easy to assume the yoga caused it. What the yoga did do, I think, was get my body moving and processing and enabling what needed to happen, to actually happen.
That's why some say don't practice for the first trimester. Risk of miscarriage is highest and the teacher would rather not get the blame, even if, as it very likely, the yoga has nothing to do with it.
The no1 reason for miscarriage is an abnormal embryo. No type of exercise will change that. It's either normal or it's not.
That said, though I practiced happily throughout my first, natural, pregnancy I may not during the first trimester with the next.
Multiple chemical pregnancies, a miscarriage and nearly a year of fertility treatment have taken their toll. I'll se how I feel but may avoid classes in my first trimester, just for peace of mind.