If they are from your insurance company then Yes. If they represent the other side then No.Under all insurance policies you have an obligation to cooperate with your own insurance company. So yes you must talk to your own insurance company or they can legally stop providing you benefits.
However, you have no such obligation to talk to the other side’s insurance company and in most cases should not talk to them unless your attorney is present and even then I do not recommend it. The reason is that these adjusters are trained in questioning and they’re seeking to diminish or do away with your entire claim. You certainly don’t want to talk to them while you’re under the influence of any medication while you’re still in a hospital or anything like that. That does not mean be rude, just politely tell them that your still treating and you have not decided if you are going to hire a lawyer or not.
Remember that the insurance adjuster for the other side will be looking to protect their insured by hurting your case. Do not let them pressure you into thinking you must help them.