How do I stop

[MinnesotaRuss]

apostles and missionaries from other civs from roaming my land? What short of war can I do?

 

[Victoria]

apostles and missionaries from other civs from roaming my land? What short of war can I do?

You really should finish the title, it is a bit of click bait in its current form.
I am sure many countries have asked this question in both the past and the present. You cannot stop them with magical cards IRL nor can ye in the game. even the might of Rome could not stop something that hungry lions would not eat.
Some choices

1. You have you own religion in which case you need to have some jolly good debates with these intruders in your great halls and also get some inquisitors to gently discuss such disbelief with your populace.
2. You have a prophet you have not used yet. Let them come, let them convert, let them wear themselves out a you build shrines and temples. Then when you are ready and have enough faith, let thine prophet fortell the future. all your cities with holy sites automagically convert.
3. You have no religion, let them come. Ease their passage so they leave. Waves of apostles and missionaries are rare and a little annoying for builders and great people but not for your military, just let them convert and leave. If it gets too annoying or it looks like they will win either admit defeat of declare them to be false with a jolly good thrashing.

 

[Spartacus73]

I thought it was going to be "How do I stop...playing Civilization?"

 

[tetley]

I like it when the heretics come to me. Buy apostles and take them out. Your holy sites are right there to heal.

 

[Moosus Maximus]

Build holy sites like you would encampments, at choke points. Station an Apostle there. Any passing religious unit will fight you, and you have the +value of the Holy Site boosting your Apostle.