As a study, this whole idea is very interesting. Much like the somewhat related "isolationist USA"-idea, this kind of concept allows one to consider in which ways and to what extent a purely-white-(protestant-)from-the-outset USA would differ from the OTL USA. Of course, there's a difference between "ASBs make the Americans decide to deport all non-whites, let's go from there" and an attempt to make a realistic scenario.
Here's the thing: the southern states aren't going for this. Not ever. The idea of supporters of such plans setting up a Colonization Society was all fine and well, but the idea of a the federal government forcing slave-owners to sell their slaves to the state (presumably at a state-determined price) and the taxpayers being forced to pay for the setting up of an African colony just to get rid of the ex-slaves? That's going down like a lead balloon. So if you want to play out a "this just happens, imagine what it'd be like"-scenario, that's fine, but be aware that it's ASB.
That doesn't mean that a USA carrying out this kind of scheme in the 1780s cannot exist. It'll just have to be a USA without the slave states. It is not altogether impossible to imagine a USA with a POD quite shortly before the revolution, which leads to the revolutionaries (or at least those in the north-east) having more of a nativist streak. One can imagine the sudden upsurge of a popular religious movement, based on the actions of some ATL firebrand preacher from New England. Have him fulminate about the protestant destiny of the USA, the danger of foreign evils, the fact that slavery is a sin, and that "America is for the white protestant, just as Africa is for the black man"... etc. etc.
Assuming such a religious movement gains traction and becomes intwined with the (northeastern) revolutionary movement, you've got your basis for a whole bunch of north-eastern states in a (just slightly) ATL USA wanting to enact policies of nativism, pro-protestantism, anti-slavery and deportation-of-blacks. This will soon clash with southern interests, and one may assume that the USA falls apart into two distinct regions, presumably along a border following the Mason-Dixon Line and the Ohio river. To the south, you'll see a CSA-avant-la-lettre, although perhaps with a bit more Jeffersonian romanticism and with less fire-eating fanaticism (because the whole conflict with the north is settled with an immediate split, before it has time to fester).
To the north, however, we get the very white alt-USA that this thread is about. It's nativist right from the start, and it has to be, or future immigration will just turn it into... well, into a normal country. Its politics are opposed to immigration, excepting protestants-- so basically, there will only be immigration from Britain, the Netherlands, Germany and Scandinavia. Catholics, Eastern Europeans and non-whites of whatever variety need not apply. Religiously, it's going to be fervently protestant and anti-catholic. Despite some claims that there were many catholics in the northeast at the time, this was decidedly not the case. Anti-catholic policies would only be an extension of exiting pre-revolution norms. Needless to say, slavery is going to be abolished: on the one hand because it's seen as sinful (and one should not be surprised to see usury get outlawed, too), and on the other hand because slavery means there are non-whites, and this alt-USA wants those gone. Fortunately for those who want that, there are rather few blacks in the relevant states. These get bought up by the government, and deported to (alt-)Liberia.
There are two possible futures for the alt-USA I've sketched out here. In one of them, it eventually just mellows out, relaxes its restrictions on immigration and religion, and becomes (as I mentioned before) what we'd call 'a normal country'. In the other scenario (and that's the one we must explore to actually keep it all ethnically white), it keeps itself closed off. It stays fervently protestant. It stays staunchly nativist. It becomes, almost by design, a closed-off and isolated country. It has less manpower, because it has a smaller demographic base to start with with, and (far) less immigration. There's anouther country between it and the mouth of the Mississippi anyway, so the OTL motivations for the Louisiana Purchase (gaitning control of New Orleans) are not present. I doubt this alt-USA is going to expand much, if at all. This is the kind of place that would rather be 'pure' than gobble up lots of lan filled up with dirty foreigners. This alt-USA is more likely to be a hermit kingdom than an expansionist empire.
The conclusion I draw from all this is that you cannot keep a country from changing except by implementing policies that forcibly keep things as they are. This whole ethnically homogeneous 'white USA' doesn't seem at all pleasant to me. There are probably people who imagine that kind of thing all too fondly, of course. Bu what I see is a USA that is smaller, meaner, bleaker-- less in every way. This is a monochrome country. It has no Notre Dame University. No Jazz or Blues. No wildly varied cuisine adopted from dozens of countries. This America will never elect a John F. Kennedy. It celebrates no St. Patrick's Day. Its New York City is utterly devoid of Italian-Americans. We can't really get a feel for its potential socio-economic dimensions, but somehow, I imagine this country's spirit as the malformed spawn of the Salem witch trials and the Great Depression.
Yes, this sort of scenario is very interesting to investigate-- but only in a theoretical way, thank you very much.