An interesting side bar to this is that, for the most part, English colonies removed the natives (Canada, US, Australia, NZ), while Spanish (and Portugese) Colonies interbred with them. We can see where those colonies are today, and I am not implying the policy is the reason. But the reason for the disparity is a good topic for a future discussion.
Note that some interbreeding also happened in the north, like in Canada with the Metis. But in general the settlers in the English colonies kept away from the Indians
I believe it had a lot to do with the actual mechanics of the respective "European" presence. In the Spanish controlled portions of the New World, they arrived specifically for the exploitation of the people and for the resources, especially gold and silver. The Spaniards never so much wanted to settle the land. It was easy, even in relatively small groups, through force of power, to get what they wanted, including many native women. IMO many Spaniards saw their time abroad as part of their duty and the cost of doing business.
The English and French on the other hand, came to settle. Sure in the beginning exploitation may have been the motivating factor, but lack of gold and silver lead to a change of plans. Indians were displaced by sprawl over time. Early settlers on the frontier were at the mercy of the natives. Sometimes it was peaceable sometimes not. These settlers brought their own women had had little need to "take" native women, besides due to their small numbers the Indians would have easily wiped them out for trying. I'm sure interbreeding occurred, just on a much smaller scale than the horny Spanish soldiers with nothing better to do with their free time.
