Quoted:
What I'm getting at
Dress up like a military member = protected by the 1st amendment
Dress up like a cop = illegal
Generally speaking, dressing up like a cop is also protected by the 1A. The part where it becomes illegal in every jurisdiction I'm familiar with is when you use the appearance to issue directive to others under authority you do not posses.
Relevant TPC section:
Sec. 37.11. IMPERSONATING PUBLIC SERVANT. (a) A person commits an offense if he:
(1) impersonates a public servant with intent to induce another to submit to his pretended official authority or to rely on his pretended official acts; or
(2) knowingly purports to exercise any function of a public servant or of a public office, including that of a judge and court, and the position or office through which he purports to exercise a function of a public servant or public office has no lawful existence under the constitution or laws of this state or of the United States.
(b) An offense under this section is a felony of the third degree.