Do people actually think that?
To be clear, trans people do not have a legal route to leave their old name off a DBS application, and therefore hide any past criminal activity.
Trans people fill out the same DBS form as everyone else. On that form, it is clear that they must include all past names. If they do not then they are committing fraud.
What they can do is then have the past name redacted from the final certificate, so the employer or organisation will not see it. But all past crimes are shown (if the type of check means they should be shown).
There is no legal route for trans person to fill out the application for a DBS check and leave off their old name from the checking process.
Obviously people can do that. But anyone can. Anyone who has changed their name can leave off their old names, and only send in documentation to support their new name in an attempt to hide criminal convictions. But this is fraud, for trans people or non-trans people. It is not made possible because trans people exists; there have been name changes for a very long time before any trans polices. Criminals have been changing names and lying to DBS for a long time in the hope it doesn’t get picked up. And DBS isn’t really fit for purpose so it can work. But that’s nothing to do with trans people, and trans people do not have permission to do it.
There are many other issues around trans people changing birth certificates and other things, but none of that has any bearing on a DBS check. If they fail to give their old names then it is fraud.