The roles included providing training to teachers in local schools on sex and relationships education.
Christina Meadows, Luton branch secretary for Unison, said pregnancy rates had been falling in the borough for the past five years.
"We have huge concerns about both the posts being axed," she said. "We don't think a proper consultation or scoping exercise has been carried out and don't think the budget figures produced by the authority stand up.
"All we can say is they obviously don't regard this as an important service."
A spokeswoman for Luton Borough Council confirmed that the two roles are going.
She said the post holder for sex and relationships education was on a fixed-term contract until 31 March and would be leaving the authority to take up a new post on 1 April.
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