Problem is not meeting trans people per se. My daughter has trans friends and I have met them they are perfectly lovely kids. Although it slightly baffled me when the 17 yrs old trans biological male child said I cannot wait for my period to start. But in terms of societal changes and conflict trans men are not problematic. Trans women however, are. There are several huge issues.
Many predatory men will use trans identity as a gateway to gain access to women and children. It is just a fact as peadophiles used the church or school and places of organised children's activities to gain access to victims and offend. People who defend the trans id lobby will say it is not the trans movement and trans people's problem. But it is the problem of trans women and the community because the vast majority of trans women are intact biological males who never intend to transition and the entire community gets tarnished by the behaviour of the infiltrators. Women cannot tell apart the good guys from the bad. So the more rapists infiltrate the gender id movement the more problematic this will be for women and their children.
The fact we dilute the category of woman harms sex-based rights and protections that are enshrined in law. The biggest problem is that maintaining that trans women are women requires complete ignorance of biological reality. Female of our species does not have a penis as the male of our species does not have a vagina. There are chromosomal disorders that create ambiguities at times but those have serious issues for the sufferers. Sterility, shorter life expectancy etc. denial of basic biology gives rise to idiocies like the Scottish College of Midwifery manual giving instruction to midwives on how to catheterise a penis during the birthing process. They withdraw it but not before they were the laughing stock of the world. Are we really ready to deny basic biology to pander to the trans lobby?
Militant trans women threaten rape with their "girl penises". Those who are heterosexual when they transition rebrand their sexuality as lesbian and demand lesbians to accept having sex with male bodied individuals to avoid bring labelled transphobic. It is sexual coercion. In effect they deny lesbians the very right to sexual preference that they reserve for themselves.
It will also skew rape, peadophilia and violent crime statistics. Trans women retain male pattern offending behaviours. Recently a hospital denied there was a rape on an all-female ward because women cannot rape right? Turns out it was a trans woman patient who raped another Cis female patient. I have not even scratched the issue of female sports, violence of the trans lobby to silence anyone who reminds them of the existence of biological reality, the harm done to children and detransitioners who do not fit the narrative or the biological impossibility for man to breastfeed without endangering the baby.
I don't care what you are, how you identify. You can id as a bird, a plane or Batman. But do not expect reality to bend to your will and indulge your phantasies. This is much more than about meeting few trans people and recognising how oppressed they are. If trans people would be happy to be trans, as many of them actually are, this would not be an issue. It is militant trans women and their allies who are the problem trying to force women to allow the basic category of woman, mother etc. to be diluted, grotesquely disfigured and erased endangering women's safety and very identity in the process.