You don't get a choice of 365 days in the year for a christening. I'm currently trying to book one and was met with a sucking of teeth over the phone.
Unfortunately this year your birthday falls on one of the available dates. My DC's birthday sometimes falls on mother's day. I don't have a hissy fit about it. What can I do? My grandmother's birthday is on Christmas day and although quietly pissed off about it, she doesn't refuse to celebrate Christmas.
A close relative of my DH didn't come to our wedding because it clashed with a family birthday. Thinking about the number of attendees at a wedding, it would be unusual not to clash with someone's birthday, anniversary or similar. Now that I think back, my uncle and my step grandfather both had their birthdays on my wedding day. They both came, and I gave them both a big birthday kiss on the cheek and a hug.
Their religion has little to do with it, because they are entitled to perform the ceremony as related to their culture; they could have a humanist naming ceremony at home and the date still wouldn't be right for someone.
The age of the child, I'm not sure why you mention it - is it because well, if the child has got to two, they had just as well wait a bit more? This seems churlish on your part.
The fact is they have chosen to invite you. You should be flattered - I have received zero invitations to christenings for even the children of friends I would consider close. At the end of the day, you aren't obliged to go.