dont they (priests ect) allready have the ability to refuse to marry whoever they choose not to?

i watch 'the doctor blake mysterys' and the doctors GF/Fiance is a divorcee and her church (priest) refuses to allow her to be remarried in their church.

i know its set in the 50's so maybe they changed it.

just if they can refuse because someone is divorced why couldnt they not marry someone because they are gay?