Before desegregation in the 1960s, men and boys in most states as well as all YMCAs went swimming nude. Desegregation was in race (whites & blacks), but also gender (outside of bathrooms and dressing areas). Then concept of modern swimwear is to wear the minimum fabric needed to cover the genitals - to minimize negative impact on sanitation and swimming performance. This would be Speedo briefs or very short swim trunks for men and bikinis for Women. Then synthetic fabrics started becoming more readily available, reducing the negative sanitation impact of wearing more fabric in swimming pools, so modesty has a little more influence in swimwear, but not much. Skintight one-pieces are for women who wanted a tiny bit of modesty, boardshorts for men. Speedo briefs got some bad stigma in America due to classical / associative conditioning from their abuse in the gay movement, so the norm for men is medium-length swim trunks or boardshorts (skintight jammers for competitive swimmers that don’t want to wear speedo breifs).
Most of the answers are assuming you are asking because you prefer swimming nude. If you actually want more coverage / modesty your swimwear, these would be your choices
Fully society compliant:
Wear a skintight or near-skintight once-piece (women) or boardshorts (Men)
Mostly society compliant:
Wear a tankini (Women) or an explicit swim shirt or rashguard over boardshorts (Men, usually skintight)
Non-compliant but pool-rules rejection should be low and is very convenient (Partially society compliant for men)
Wear loose fit or fitted fit athletic t-shirt and shorts made from moister-wicking polyester microfiber (Dri-Fit, Climalite, ClimaCool, etc..) - both genders. This should be satisfactory for most modesty-concerned christian and jewish denominations.
Non-compliant, moderate rejection
Wear a burkini (women - typically muslim). If you think burkinis are too ugly or you are a man that wants full body coverage (Thais that don’t want to tan, scandinavians that sunburn red in mere minutes and don’t want to use chemical-laden sunblock), then wear a warm-up suit / tracksuit made from moister-wicking polyester microfiber (Dri-Fit, Climalite, ClimaCool, etc..)
Brands for wick-wear microfiber polyester (athletic clothing):
Nike: Dri-Fit
Adidas: Climalite, ClimaCool (ventilated), Clima365
Under Armour: HeatGear, threadborne (not charged cotton)
Champion: Vapour, X-Temp (Double-Dry is older and not very good)
Swimming in public pools and water parks in full street clothing without rules rejection is only viable in southeast Asian countries - Vietnam, Laos, Cambodia, Thailand, as well as Pakistan, parts of India, and parts of Indonesia. Pakistan regular street clothes in the water parks is the norm, wearing anything less than athletic clothing (t-shirt/jersey) will have rules rejection issues. China, Korea, Malaysia they cover up more but you can’t wear regular street clothing, must be athletic clothing or more-coverage dedicated swimwear. India is the closest you’re going to get for a free-for-all (does not include nude) where some will be fully clothed, some even wearing shirt & tie, and some will be dress-down (athletic or modest-swimwear or undershirt & boxers or undershirt & regular pants/shorts) and some will be in western-standard swimwear. For out-of-water comfort reasons, and practicalities, it is best to stick to athletic or more-coverage dedicated swimwear (Malaysia trend, and South Korea). Denim jeans, woll shirts, linen pants and shirts take forever to dry, drip water everywhere, lint excessively and color-bleed in chlorinated swimming pool water. Microfiber polyester ‘dri-fit’ athletic clothing and dedicated swimwear are more comfortable to wear wet and let dry on you.
The nudists will have the most luck in the Speedo countries of Europe - Spain, France, Italy, Portugal - they have a large quantity of nude-permitted beaches. Parts of Brazil has some too.