It depends how i meet them. If i just meet them randomly by chance, then its fine because i can just leave and have no obligation to speak with them or develop a conversation since we didn't meet intentionally, but if its an arranged meeting, such as a friend tells says let's go somewhere and these other people will be there too, then i feel very anxious because then the meeting is intentional and there is a social standard of talking and getting to know people you intentionally meet.
I'm not a very social person, i am not able to open up and be talkative with people i don't know, so when i have to go and meet people i just don't really have much to say, so its an awkward situation, and this causes me to be anxious about meeting them in the first place.
It also depends on the person though, some people i can get along with very easily from the start and find it easy to open up to and actually find a topic of conversation with, but the initial feeling is still anxiety.