You should not talk to the other insurance company unless your insurance agent instructs you to do so. Your insurance agent's primary goal is to save their company money, which means assigning as much of the blame and responsibility to the other driver. The other insurance company has the same primary duties to their company and their customer, e.g. they are trying to save their company money and assigning as much of the blame as possible on you so that your insurance company will have to pay as much as possible for the damages. If that happens, your insurance company is likely to raise your premiums or reduce your benefits or if you are costly enough, drop you as a customer.

In an auto accident, treat the insurance agents like you would lawyers in a civil court case. You want to give your story to your insurance agent first and have them instruct you how best to handle it. It is in both of your best interests to involve your insurance agent as much as possible as a liason to the other insurance agent.

You could go through your own carrier and pay the deductible then they subrogate against the other carrier. Then they go to mediation if they don’t agree on fault. That is binding. It sounds like you live in a state that has comparative liability and the other carrier deemed you partially at fault. If they had no other reason to question that then yes they’re not going to pay you anymore.

Were there witnesses, a police report, etc?

The insurance companies speak to each other.

I have a general question.
If involved in an accident/collision with another vehicle, is it a good idea to speak with the other motorist’s car insurance when they call/text me??

Should I let my own insurance communicate with them since that is what I am paying them for?
Does talking to the other insurance compromise my case?

I followed this advice and ignored the communication of the other driver’s insurance.
They then only accepted 50% liability (no more) so am wondering if my refusal to respond to them affected their final decision.