There's little question there are similarities between Marvel's X-Men and DC's Doom Patrol, as Stan Lee was accused by the latter's creator Arnold Drake of ripping him off. In an interview with Newsarama in 2005, Drake admitted over time he became "more and more" convinced that Stan Lee "knowingly stole the X-Men from the Doom Patrol." So are Marvel's mutants a rip-off of the Doom Patrol? There doesn't seem to be a definitive answer, but there are unquestionably some similarities between the two groups of heroes.
Doom Patrol and X-Men both debuted in 1963 and shared similarities from the getgo. Chief, Negative Man, and Robotman debuted in My Greatest Adventure #80 by Arnold Drake, Bob Haney, and Bruno Premiani, while Professor X, Jean Grey and Cyclops debuted in X-Men #1 by Stan Lee, Jack Kirby, Paul Reinman, and Sam Rosen three months later. Both comics featured a wheelchair-bound genius running a team of superpowered outcasts serving as an allegory for real-life issues, including the Civil Rights movement and the treatment of minorities. While the Doom Patrol achieved moderate success, the X-Men would become one of the most popular superteams in comics. But, did Stan Lee rip off Doom Patrol?
The comic's similarities have always been a point of contention. Doom Patrol creator Arnold Drake did an interview before he passed in 2007, where he admitted over the years, he became "more convinced that [Stan Lee] knowingly stole The X-Men from The Doom Patrol. I didn't believe so in the beginning because the lead time was so short [Doom Patrol's first appearance was in June 1963, X-Men number one came out three months later]." Drake added he learned multiple writers and artists were working with both DC and Marvel at the time, so they might have overheard his story and made their way back to Lee.
Drake said Lee might have had a 4-6 month head start after learning about Doom Patrol, potentially squashing the idea that the Marvel icon didn't have enough time to copy his idea and put it to print. Interestingly enough, it's been suggested the Doom Patrol were actually inspired by the Fantastic Four. So it's possible inspiration was borrowed from both Marvel and DC? Marvel had no problem joking about the controversy, calling a parody version of the Doom Patrol the "Ecchs-Men" in an issue of Not Brand Ecch.
To make matters even more complicated, it turns out the character the Negative Man, was published by DC Comics back in 1959 in House of Mystery 84 - and was penciled by X-Men co-creator Jack Kirby before the Doom Patrol ever came to be. That character had similar powers to the Doom Patrol's Negative Man and is often referenced as the prototype for Drake's creation.
Honestly, it seems like Arnold Drake has a case that the X-Men were at least influenced by the Doom Patrol. However, there's no concrete evidence it was done maliciously. Stan Lee could have heard about the Doom Patrol and used them to inspire his own heroes, but as the legend goes, Drake could have been inspired to create those heroes based on Lee's Fantastic Four. Both creatives seemed to draw inspiration from their Marvel/DC counterparts. In this case, we're glad both the X-Men and Doom Patrol exist despite their controversial connective tissue.