changing the value of one combobox causes the value of the other one changes

Here are two ways to avoid this issue.

Solution A：

Use BindingSource as the DataSource of ComboBox.

recieverComboBox.DataSource = new BindingSource(myDataSet.Tables[0].DefaultView, null);
recieverComboBox.DisplayMember = "UserPosition";
recieverComboBox.ValueMember = "ID";

recieverUnReadComboBox.DataSource = new BindingSource(myDataSet.Tables[0].DefaultView, null);
recieverUnReadComboBox.DisplayMember = "UserPosition";
recieverUnReadComboBox.ValueMember = "usr_Id";

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Solution B:

Call method DataTable.Copy

recieverComboBox.DataSource = myDataSet.Tables[0].Copy();
recieverComboBox.DisplayMember = "UserPosition";
recieverComboBox.ValueMember = "ID";

recieverUnReadComboBox.DataSource = myDataSet.Tables[0].Copy();
recieverUnReadComboBox.DisplayMember = "UserPosition";
recieverUnReadComboBox.ValueMember = "usr_Id";