No, you must not screen participants out of your survey based on criteria which is not specified using Prolific's prescreening options.
By this, we mean that the full eligibility criteria for your study must be applied to your prescreening, so that all participants who are sent to your study can complete it and receive the reward. You cannot simply reject participants if they do not meet the criteria you're looking for, or exit them from your survey, if the criteria wasn't applied to your prescreening (see step 4 here).
It is very frustrating for participants to get unexpectedly kicked out of studies, and our platform has been designed to help you recruit only the specific sample that you require for your study.
If you want to recruit a niche demographic that you can't obtain using our existing prescreening filters, please refer to the following help article: Recruiting a niche sample with custom screening requirements.
For example, I'm a researcher who only wants to recruit individuals whose favourite flavour of ice cream is chocolate. However, I could not simply publish my study, ask the question in my survey, and reject any participants who respond that their favourite flavour is vanilla or strawberry (or exit them from the survey).
As there is no existing screener related to participants' favourite ice cream flavours, I would instead have to run an initial screening study which contains the question:
"What is your favourite flavour of ice cream? Vanilla, Chocolate, Strawberry...etc."
Once I've collected the data from this initial study, I will have a list of Prolific IDs that match my desired screening criteria (i.e. any participants whose response is "Chocolate"), and can invite them to my main study using a Custom Whitelist.