If someone commits an act, which could be seen as 'Istihzaa bideen' (mocking Islam), does it mean they are then Kafir and no longer Muslim?

Praise be to Allah, the Lord of the Worlds; and may His blessings and peace be upon our Prophet Muhammad and upon all his Family and Companions.

Mocking religion is Kufr (disbelief) that drives the person out of the fold of Islam whether the mocker is serious or joking. Allah says {If you ask them (about this), they declare: "We were only talking idly and joking."Say: 'Was it at Allah, and His Ayah (proofs, evidences, verses, lessons, signs, revelations, etc.) and His Messenger that you were mocking?' Make no excuse; you have disbelieved after you had believed. If We pardon some of you, We will punish others amongst you because they were Mujrimûn (disbelievers, polytheists, sinners, criminals, etc.)}[9:65-66].

So mocking takes the person out of the fold of  Islam; whoever has done so, must repent to Allah and seek His forgiveness. Allah loves the people who repent and accepts their repentance. Allah says: {And He it is Who accepts repentance from His slaves, and forgives sins, and He knows what you do.}[42:25].

Allah also says: {Truly, Allah loves those who turn unto Him in repentance and loves those who purify themselves (by taking a bath and cleaning and washing thoroughly their private parts, bodies, for their prayers, etc.)}[2:222].

Committing an act of disobedience is not limited to mocking the religion, because a Muslim can be disobedient as a result of being overwhelmed by desires and following the steps of Satan and so on.

Allah knows best.