I think I read somewhere that before VII, or at least right after Trent, it was customary to conditionally baptize all protestant converts. Is it true?

NOTE: I know that anybody, even a raging heretic, can confer a valid baptism provided that he observes the matter and form and has the right intention. That's what the theory says, in practice, the Church could not trust the intention of protestant ministers and their observance of matter and form was always put into question due to their general heterodoxy and lack of reverence for the sacrament. Also, it would be very costly and time consuming to investigate validity case by case. I think that was the rationale.

there is the possibility of New Order not baptizing.  NO may have the intention to initiate.  Ask what the purpose of Baptism is?  If Original Sin is not the intention, then there is your answer.

In the first edition of 'The Ceremonies of the Roman Rite Described' (1917) Dr Adrian Fortescue suggests conditional baptism of converts was very common, if not the norm:

'The commonest case in England is that of converts doubtfully BAPTIZED. Such a convert makes his public profession of faith and abjures heresy. He is then baptized conditionally (the condition is expressed), privately with holy water (not baptism water). Then comes the absolution from excommunication. But if it seems more convenient, the private baptism may follow the absolution from censures. Then the convert mades his first confession.'

When I was received, at a conservative NO parish in 1982, I was conditionally baptised, having gone through an Anglican baptism service where the minister did not pour water but made the Sign of the Cross on my forehead with it.  My understanding is the practice of conditional baptism was increasingly frowned on as modernism took hold as 'insulting' to non-Catholic communions and would be very rare now.