We have to examine what “tabiqiyyah” means. One example of it is the way Sunnis wear their turban. The Shia turban has 2 ends, whereas the Sunni one doesn’t, and if you untie the first part it falls apart. Not the Shia one.
Yes it’s highly recommended to have the hanak under the chin while praying or traveling. I’ve seen many scholars do that while praying.