All perfect praise be to Allaah, The Lord of the Worlds. I testify that there is none worthy of worship except Allaah, and that Muhammad is His slave and Messenger.
First of all, it should be noted that the scholars clarified the showing off that is dispraised, and Ibn Hajar Al-Haytami said: "Showing off that is dispraised is when a person intends to gain the pleasure of other than Allaah when doing acts of worship, like when he aims at people to look at his act of worship, and see that he is perfect, so that he may get from them money, fame or praise.”
Hence, showing off is related to acts of worship and not to matters of customs and traditions.
Therefore, it becomes clear to you that if a person wears nice clothes so that people would see that it is nice, without him being proud and conceited, then this is permissible. Similarly, if he does not wear those clothes out of fear that people would dispraise him, then this is permissible.
The same thing applies to a person who avoids using a particular kind of mobile phone; this is not showing off. Rather, if he abandons it because the customs indicate that it is particular to women, then this is a praiseworthy act from him and he will be rewarded for it, Allaah willing, if he does so for the Sake of Allaah.
Allaah Knows best.