baptism was never restricted to the parish church - eg Roman Catholic baptisms - what was required in 1849 was for the registers to be copied across to the Rolls office.
What was controlled by 1753 Marriage Act was that marriages must be in the Parish Church (or other church by Bishop's licence) but to be married you had to be confirmed (again exceptions needed Bishop's licence) but to be confirmed you needed to have been baptised - though Catholic baptisms were recognised.
The 1849 act effectively recognised Roman Catholic marriages and opened way for marriages in Methodist Chapels