Q: Why does Data put on the purple clothes? After Kivas hits Data with the acid in "The Most Toys" (https://memory-alpha.fandom.com/wiki/The_Most_Toys_(episode)), he presents the android with a choice: run around naked, or change into the purple clothes which were refused earlier.
Data chooses the latter option. What is the in-universe reason for this? Data did not want to put the clothes on earlier, and he wouldn't be embarrassed or cold if he was naked. 
I guess the most reasonable explanation is that Data, as a Starfleet officer, would want to emulate a typical Starfleet officer in that situation. And the proper thing to do would be to appear presentable, even if it meant donning undesirable clothing. 

A: In the 7th season episode "Inheritance" we find out that Data has a modesty subroutine.  When Data was first constructed, he didn't feel the need to dress because he didn't "suffer from the elements", but some of the colonists were disturbed because he was anatomically correct.  
Data would not willingly change into the clothes that Fajo wanted him to wear but with his uniform gone, he changed into what was available rather than remain naked (and again depriving Fajo of any cooperation). 

A: Kivas Fajo suggests that Data will probably follow the rules of decency prescribed by Starfleet training:

FAJO: Oh, don't worry. The solvent won't harm your, your skin. But in seconds it will completely dissolve that uniform. Personally, I'd be delighted to see you go around naked. I assume you have no modesty. But, then, I guess that decency is the rule of your Starfleet training.

Data does not correct Fajo on his assumption, which is significant as Data had already refuted Fajo several times, such as:

FAJO: I think you should be flattered.
DATA: I am not, sir. Most intelligent lifeforms find involuntary confinement offensive and inequitable. Moreover, you have violated Federation law.

As Data doesn't debate Fajo on the Starfleet decency point, we can assume that Data wore the purple clothes for the reason suggested by Fajo.

A: He is acting like a Starfleet officer (or human being)

FAJO: Well, it doesn't matter. It isn't true anyway. My father was
  quite wealthy, actually. He was a thief. Data, why don't you put on
  these lovely new clothes and sit on the chair. 
DATA: I must decline. 
FAJO: You are going to be much more of a challenge than I had first
  thought. (goes to replicator) Finoplak, one hundred denkirs. (A vial
  of liquid appears.) Now, Data, in the meantime, here is something for
  your logic circuits to analyse. (Fajo throws the liquid onto Data's
  uniform, which begins to smoke and dissolve.) 
FAJO: Oh, don't worry. The solvent won't harm your, your skin. But in
  seconds it will completely dissolve that uniform. Personally, I'd be
  delighted to see you go around naked. I assume you have no modesty.
  But, then, I guess that decency is the rule of your Starfleet
  training. In any case, Data, why don't you make a decision about which
  alternative you dislike the least. Make a decision by dinnertime
  tonight. I have invited a guest to meet you, and I expect you to be as
  entertaining with him as you have been with me.

Of course, this is merely Fajo's (perhaps rather biased) assessment of Data's personality. But it agrees with yours. Data  has no modesty, in the sense that he is not embarrassed to be naked. But he does have decency, in the sense that he prefers to conform to the social norms surrounding nudity. 
As a Starfleet officer, presumably he is supposed to remain dressed at all times. As a human being in polite company, he is supposed remain dressed. Either way, whatever his personal preferences, he will accommodate human norms and remain dressed.
He really does feel "embarrassed" to be naked
Something else to consider: the entire episode is about Fajo treating Data like an object, not a conscious being. Perhaps we are supposed to see Fajo as wrong here, and Data as being sufficiently "human," or at least sufficiently similar to the humans he hangs out with, to prefer, of his own accord, being dressed to being naked. 
Indeed, the episode "Inheritance" (S07E10) suggests that this may be the case. 

JULIANA: That was nothing to the problems we encountered. Never mind.
  I don't want to embarrass you. 
DATA: I am incapable of embarrassment. Please continue. 
JULIANA: Well, the one thing we couldn't anticipate was that you
  didn't seem to mind about being naked. Some of the colonists objected
  to having an anatomically correct android running around without any
  clothes on. We asked you to dress, but you didn't feel it was
  necessary because you didn't suffer from the elements. We actually had
  to write a modesty sub-routine to get you to keep your clothes on.

