Trying to get some context here; what exists in your lives that remains common together and hence necessary you remain in touch? Children? Pets? Friends and acquaintances? I am just saying that there are legitimate reasons two ex-partners would remain in communication. However, if such things don't exist then there is no reason to do so. I like the mention of blocking but before doing so I guess I would offer up explanation and an advisement I was going to take such steps. Doing so need not be difficult; a simple text of your own, "Look you are making me uncomfortable, I won't accept any more communication from you" should suffice.

Let us know what you decide.