Pairs sharing a leg are related by construction. EUR/USD and GBP/USD both contain a short dollar; AUD/USD and NZD/USD share both a dollar leg and a common commodity and risk-sentiment driver. Long all four is one large short-dollar position dressed as diversification.
Correlations are measured over a chosen window and they change with it. A 20-day reading and a 200-day reading on the same two pairs can have opposite signs, and correlations tend to rise toward one precisely when it hurts, during a flight-to-quality.
The practical control is to size on aggregate exposure per currency rather than per pair, using notional-exposure converted into the account currency. Netting the legs first shows what you actually own.
Example: four longs of 0.5 lots in EUR/USD, GBP/USD, AUD/USD and NZD/USD is roughly 200,000 units of short dollar exposure. A 1% dollar rally costs about 2% of a $100,000 account, not four small independent losses.
Related: notional-exposure, correlation, portfolio-heat, commodity-currency