Didn't eat red meat while pregnant or breastfeeding - question

About two years before becoming pregnant I stopped eating red meat for multiple reasons and the main one being that I felt sick to my stomach after eating it. During pregnancy I tried to eat a burger and I felt terrible after and threw up. Another time I tried a tiny bit of red meat in pasta and the same thing happened. I haven't tried after that and I think I'm done trying. That being said - can my baby eventually eat red meat (no red meat throughout pregnancy or breast feeding) ? Is there a reason why he may not be able to? My friend said that her mother was a vegetarian while pregnant with her so she can't digest meat herself