The statement is accurate:
10 of the 11 U.S. recessions between 1953 and 2020 began under Republican presidents.
The only exception in that period was the recession of January-July 1980, which started under Democratic President Jimmy Carter. The other ten recessions since 1953 have started under Republican administrations, specifically Eisenhower (three times), Nixon (twice), Reagan, George H.W. Bush, George W. Bush (twice), and Donald Trump.
Economists Alan Blinder and Mark Watson found that the U.S. economy was in recession for a significantly larger number of quarters under Republican presidents than Democratic presidents during the 1949-2013 period they studied (41 quarters vs. 8 quarters). While the data clearly shows this disparity, the reasons for it are a matter of ongoing debate among economists and are influenced by various global and domestic factors, such as oil price shocks and inherited economic conditions.