I think you are safe to eat parsley in that sort of form and in small-medium amounts.
Parsley OIL is probably not safe - but this is very concentrated... so you would have ot eat bunches and bunches and bucnhes of parsley for there to be an issue.
I was very careful with food when i was pg (figured it was only a short period of life) so I did avoid things like taboulli that are mainly parsley (though am pretty sure even that would be ok) but i did eat things that had parsley in just as a herb (e.g pizza sauce base etc would be ok)
I am not a dr though, so maybe someone else has some other ideas...