"...some men, not even near all, are not safe to have custody..."
That goes both ways.
"...some women deliberately trap some men they know are not the father..."
Some women deliberately trap some men to make them a father.

To sum up: keep in your pants, boys.

So the problem is men? nothing to see here we all know men put it about? well back to reality the problem is men who are not the father, not the father, being chased by mothers who sometimes know they are not the father, to comply with social welfare demands they name someone as dad, the problem is also, social welfare, that even gets court judgments against the not the father, sometimes even putting hold on bank accounts and wages, for a child that is not his, NOW if it was possible for a mum to be in that position would the court pursue her? come, DNA BY LAW for every child support case and make the stand over child support agency's return every dollar men wrongly paid, let them get it back if the can from the woman they commited a fraud for in the first place

Belly,

I have never mixed in the circles you obviously have, but I would have thought that these women wouldn't be accusing blokes they didn't know of fathering their children, and even that sort of women would not be daft enough to accuse any bloke who hadn't rogered them of putting them up the Duff. So I repeat, keep in in your pants and you won't be accused. This sort of stuff shouldn't be of concern to a bloke of your age anyway.

Some men have been paying for years, child care for children that are not theirs DNA proved this
Some women knew this all the time.
Some of these men have even had money taken out of their wages/personal bank accounts
Pursuit of these men by child support has often been traumatic.
When the truth is revealed women rarely pay back the man.
Fairness for both sexs is not a crime.
As can be seen by any one who is able to understand the parents of some children never bothered to wed

It's a hard issue. On the one hand, seeking protections on the limits of the justice system so to sort out the abuses is worth striving for. However there is another issue too. Like the point of an unintended consquence is to hold everyone's DNA data from their birth, one other unintended consquence is that mistakes happen in medical testing. If one test accidentally gets mixed up with another then there's no chance that the correct father will be identified. A mixed up test can cause a family to shatter with distrust and betrayal even if there was no betrayal to begin with.

Honestly the best advise has already been given, by ttbn. Keep it in your pants boys.