Congratulations first and foremost!
I think that the advice to invite some of the children to the park, or for a play date at your home is good.
We had a similar experience in our school - my dd was friendly with a little girl who happened to be Muslim. Her mum also wore a hijab. I was amazed at how shy she was, even though she was doing a post grad degree in the local university. She had been brought up to be reticent, and not to speak out, but it didn't translate well, as other mums thought her standoffish.
It took a while of inviting her dd to our house for her to come, and when she'd come to collect, she'd never come in in case my DH was there.
This mum wouldn't shake hands or speak to a man not in her family, and while I understood this, having worked in the Far East, it was off putting for other parents. I was quite shocked at the reaction of some mums to her hijab, and not shaking hands with a man not in her family, but I suppose you'll meet that everywhere.
In some ways it was easier to have my dd go to her house, as she could control the environment to suit herself and her beliefs, and we had lovely times, chatting, and drinking tea, when id go to pick up my dd. I played it by ear with her, and we spent a lot of time, sitting, chatting on a rug on the grass in a local park, while the kids played.
For parties, her dd would arrive after all the food had been eaten, or she asked the hosting mums not to feed her dd, that she had just had lunch etc. I was quite used to dietary restrictions and observances, having kosher relatives on my DHs side, and allergies on mine, though some mums thought it quite rude to refuse hospitality.... It can be difficult, can't it, not to step on toes?
I think the thing is to be persistent, and maybe start off with a local park to have the play dates - maybe ask the other mum along too so you get to make friends, (and that way she can admire your baby!). And see where that leads you. If your DS isn't unhappy, you're obviously doing a lovely job, and sometimes school and some after school activity, like music (an orchestra) or sport ( a team) can fulfil the social aspects of a child's life, without having to have play dates.