I wouldn't compare a Tarutaru's STR to their DEX. They have average DEX. Their STR is below average.
Still, a Tarutaru's STR isn't insurmountable, it is only an eleven point deficit compared to an Elvaan's STR. Basically, it won't kill you.
What will kill you as a Tarutaru melee is the only stat that has enough difference and importance between races to matter - HP. Also, many melee players merits HP, which negates any possible fix that could have while keeping the gap as wide if not wider.
At the widest gap you're missing 445 HP between yourself and a Galka, and this difference will get your ass killed. This wouldn't be so bad if every job had an MP pool or even every job that does have an MP pool had it make a make or break difference but the prevalence of refresh sources have made the 467 or so MP difference at the widest point (a job/subjob combination that nobody uses on a job that is arguably the most neglected job) between yourself and a Galka. There aren't any unique refresh sources to help rebalance this, and further adding insult to injury, the easiest way to start a fight with more MP is converts HP to MP gear, something a Galka can afford to do, but the opposite isn't always an option with melees without MP pools.
Any chances of this inbalance being remotely negated are pooped on by Tarutaru's low VIT, and even Tarutaru's above average AGI or INT doesn't help since it won't make you evade enough damage enough of the time or resist enough magic damage enough of the time.
So SE balances mobs to be threatening and deal about 370~595 more damage to be a threat to everyone who isn't a Tarutaru which is often lethal to melee range Tarutaru. The worst DD in the game is a dead one, so HP ends up actually mattering more then any other stat.
Despite all this I suggest you choose whatever race you want and have fun. If enough Tarutaru players complain about the imbalance we could see a change in monster actions or HP/MP numbers between races.