Maybe if Portugal would become a republic too, which would be cool even if very unlikely.
Conversely, I'd say that that would make it
less likely. There seems to be a prevailing idea among some people that for all time, states with ideas in common preferred to form federations for mutual gain. I can't think of a single time that happened. Really, the only time unions happened was when monarchs inherited thrones which technically forced a union. OK, so during the Commonwealth period there was a brief move to have the Netherlands join the Commonwealth, but this was nothing more than a political ploy. The Dutch citizens were heartily against the move - as was England - and the entire move was done only by representatives of Holland (not the whole Netherlands) in an attempt to dangle a golden goose in front of Cromwell to make him more pliable. Modern evidence seems to suggest that those responsible had no intention of going through with the deal anyway, and Cromwell rejected the offer out of hand.
Nationalism hadn't formed in this era, but there was still a prevailing sense of a country's existence. The Dutch, to use this example, knew they were different from the Portuguese, and religion is only one factor. They had different economic styles, their empires were in trade competition, they had different national values, and really aside from the military aspect of fighting the Spaniards, there would be no advantage to the two countries being united. Any military cooperation could - and was - handled by simple alliances. Of course, there is also the point that in this era, the Netherlands and England were usually at each others throats, and the Portuguese had a longstanding military alliance with England (dating from 1345 I believe, and presently the world's oldest military alliance) and this alliance surprisingly was taken very seriously for centuries. The English did help the Portuguese by sending troops to Portugal on several occasions. While I think the Dutch also aided Portugal OTL, I think any move to become closer diplomatically would have invoked the wrath of England, which would certainly put strain on the deal.