People are being urged to join the Free Conscience initiative, which is calling for a change in the law to protect conscience rights for all medical professionals.
Organisers fear current legislation risks creating a "less diverse and inclusive" healthcare system by not properly protecting staff for "unjust discrimination".
A proposed law they hope will remedy the situation, the Conscientious Objection (Medical Activities) Bill, is being discussed during a Second Reading in the House of Lords on Friday morning.
Baroness O'Loan, who has tabled Bill, said: "No one should be coerced by the risk to their careers into violating their conscience, and it is plainly inconsistent with the principles of equality legislation to exclude whole sections of society from areas of medical employment simply because of their moral beliefs."
Spokesperson for the Free Conscience campaign, Dr Mary Neal added: "There is a pressing need for statutory conscience rights which actually protect those who need protection.
"The current law fails to do this, so this Bill is a necessary and timely step."
A report by MPs and peers on the All Party Parliamentary Pro-Life Group concluded in 2016 that some doctors and nurses who oppose terminating a pregnancy have encountered discrimination.
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