What you're asking is tricky. Generally
Give believers benefit of the doubt.
O you who have believed, avoid much [negative] assumption. Indeed, some assumption is sin. And do not spy or backbite each other. Would one of you like to eat the flesh of his brother when dead? You would detest it. And fear Allah ; indeed, Allah is Accepting of repentance and Merciful.
Try and testing people
The verse is talking about believers ie people who don't believe in God, may not fear God and therefor your morals would be meaningless. In addition, some believers also may have a نفس (self) which deceives them.
O you who have believed, if there comes to you a disobedient one with information, investigate, lest you harm a people out of ignorance and become, over what you have done, regretful. Hujarat 6
It may work, but it's better to test people before:
Nahj al-Balaqa: Sayings of Amir al-Mu'menin 384
Amir al-mu'minin, peace be upon him, said: Leaning towards this world despite what you see of it, is folly, and lagging behind in good deeds when you are convinced of good reward for them is obvious loss, while trusting in every one before trying is weakness.
وقال عليه السلام : الرُّكُونُ إِلَى الدُّنْيَا مَعَ مَا تُعَايِنُ مِنْهَا جَهْلٌ، وَالتَّقْصِيرُ فِي حُسْنِ الْعَمَلِ إذَا وَثِقْتَ بِالثَّوَابِ عَلَيْهِ غَبْنٌ وَالطُّمَأْنِينَةُ إِلَى كُلِّ أَحَدٍ قَبْلَ الاْخْتِبَار عَجْزٌ
Long term affects of trusting
Having that said trusting people is generally recommended and we should avoid not trusting people the first verse says و لا تجسسوا meaning don't investigate/spy on them/ look over their shoulder IF the person is a believer. (By Qur'an we know the followers of the Abrahamic religions are believers, so we can trust them.
Similarly this research concludes trusting people will make you better at spotting those who lie:
People high in trust were more accurate at detecting the liars -- the
more people showed trust in others, the more able they were to
distinguish a lie from the truth. The more faith in their fellow
humans they had, the more they wanted to hire the honest interviewees
and to avoid the lying ones. Contrary to the stereotype, people who
were low in trust were more willing to hire liars and they were also
less likely to be aware that they were liars.
Trust your friends, but why risk it? These are two different things. Let me give you an exaggerated example: It's like walking among your friends with no scarf and saying I kindly ask you to not look at my hair. Private matters, body parts are like secrets. Don't put your secrets out in the open. Trust basically means believe what they say, it doesn't mean open up your everything with them, tell them your most intimate secrets.
Additionally I would assume that your friends would respect you. Nowadays people who have the weirdest ideologies are respected, I'm pretty sure modesty deserves more respect. Just do it in a nice and polite way and have faith that Allah will hold your back.