As frustrating as rushes are, there's a reason they are there: they are meant to counter the sorts of builder-beeline strategies that leave you vulnerable to early attack, like the strategy your friend employs. It's not like you can't defend against them, either: the Great Wall is an incredible wonder for doing so, since 1) -1 movement on enemy ranged units means they can no longer move and attack in your territory, and 2) the wonder's effects stay until the person who built it researches Dynamite, and since Dynamite is not located on a vital tech path, the person who build Great Wall can easily enjoy its benefits into the early Modern Era by simply going for Radio and Plastics before researching the part of the tech tree that Dynamite is in.
Plus it's not like their all-in strategies, either: rush strategies are typically only ever meant to conquer a neighbor or two to give you an upper hand against everyone else later in the game. Since you'll usually be going Liberty, you'll be able to make much more use out of conquered cities as well.
Very odd, since Liberty strategies usually either focus on conquering their neighbors quickly while they have the hammer advantage over Tradition players to keep spewing out military units and/or by exploiting Sacred Sites and turtling (if you have 10 cities and 2 faith building beliefs, Sacred Sites can net you +40 tourism at a point in the game where most players don't have the culture to defend against it, though you really have to make sure you keep your tourism edge because this strategy has no lategame). Builder and lategame war strategies tend to work better with Tradition, regardless of whether you have Religion or not (Tithe is always powerful, Pagodas are always good, pick up Religious Communities is incredible with the centralized production of Tradition, Temple Happiness is still good because it gives +2 just like Pagodas).
Liberty generally tends to run into gold problems a lot more than Tradition because of the way building maintenance works, and the following three ways are the best way to address it IMO: 1) always keep maintenance in mind, so don't build roads to cities whose city connection gold won't make up for road maintenance (1 pop roughly = 1 road's worth of maintenance) and build military units instead of buildings that aren't worth their maintenance, 2) Currency is incredibly important, I'll often have markets in my cities before libraries (it's better for science too, because it means less negative gold to cut into your science), 3) tribute city-states as much as you can with the army you'll end up building as a Liberty player.
I don't know why you'd want to concentrate on culture generation from a religion. The two main uses of religion are happiness and faith generation, the sole exception being Tithe. This is why religions are so important to wide/Liberty strategies: it is one of the few ways they can counter the happiness hit from having so many cities and also lets them keep up with Tradition empires' science by being able to buy a lot more Great Scientists (and research buildings, too, with Jesuit Education). At best, the culture you'd generate from faith-purchased buildings in each city is roughly equivalent to a culture specialist's worth of culture (artist/writer/musician specialists create +3 culture, a monastery + pagoda generates +4 culture), so if you're going for a tall build that would work those specialist slots anyway (Liberty cities don't tend to have the population to work specialist slots), it's better to just ignore religion for culture generation and focus on getting early guilds and wonders. Heck, you're better off just focusing on maxing out Piety and generating a lot of Great Prophets to plant for holy sites that give +6 faith, +3 culture, and +3 gold.
Plus, focusing on generating boatloads of culture isn't a good way to win in multiplayer anyway: the hammers and opportunity cost of building up a large culture income is much better spent on rushing to ideologies and information era, then winning a diplo victory with Globalization or a conquest victory with XCOM + Stealth Bombers (the former can paradrop anywhere on the map, including right next to players' capitols, the latter has 100% evasion and a gigantic range). Space victories are much slower and easier to interrupt that capitol sniping with XCOMs. Culture victories, on the other hand, also revolve around teching to ideologies and info era ASAP, then choosing Autocracy for its Futurism tenet (+250 tourism from using a GA, GW, or Great Musicians is incredible, especially since you can start generating that tourism instantly); if you make sure you don't generate any GA's, GW's, or Great Musicians before you unlock Futurism (just build up enough points in each to spawn one the turn right after you unlock Futurism), you can generate one of each every 7 turns or so, essentially giving you a +100 tourism per turn income before Airports/Hotels. If you do it fast enough, other players won't have built up enough culture anyway to counter so much tourism being shoved down their throats at that stage of the game.
