Prayer in Trousers and Shirts, Permissible!
Allah has commanded the one who wants to offer Salah to be decently dressed. Almighty Allah says:
(O Children of Adam! wear your beautiful apparel at every time and place of prayer: eat and drink: But waste not by excess, for Allah loveth not the wasters. ) (Al-A`raf, 7:31)
One is enjoined to adorn himself or herself for prayer. Unfortunately, many Muslim ignore this obligation and do not care about their dress, they may pray in their nightclothes or work clothes. In Salah (Prayer), a Muslim will meet His Lord, Who is the Most Beautiful and loves beauty, so he should be decently and beautifully dressed.
As regards your question, it is noted that scholars regard the least level of dress during Salah is covering the ‘awrah (parts of the body that must be covered). Hence, they stated that covering the ‘awrah is one of the conditions of validity of the Prayer, and it is not valid unless the ‘awrah is covered.
This is the required obligation and it does not matter whether the dress is tight or not. This is what has been stated clearly by the scholars of the various schools of Fiqh.
Shaykh Sayyid Sabiq (may Allah have mercy on him) said in his book Fiqh As-Sunnah:
“It is obligatory to wear garments that cover the ‘awrah even if it is tight and shows the shape of the ‘awrah.”
Dr. Salih Al-Fawzan, a prominent Muslim scholar, stated
If a person prays with his ‘awrah covered in tight clothes, his prayer is valid, because the ‘awrah is covered, but he is sinning by praying in tight clothes, because he has transgressed one of the rules of prayer by wearing tight clothes.”
Thus, praying in shirts and trousers, whether tight or loose, like any clothes is allowable as long as they fulfill the condition of the validity of Salah which is covering `awrah. The relation between Salah and dress is to properly cover the `awrah. It is preferable to cover the `awrah with loose clothes, whether shirts and trousers or a cloak, since this is included in the meaning of the above mentioned verse. Nevertheless, if they are tight, Salah is valid, by the will of Allah.
The claim that trousers and shirts are sign of Christianity has no relation to prayer, since what is required is the proper covering of `awrah.
May Allah guide all of us to what pleases Him!