Oil and gas companies take on most graduates for their roles who are in any STEM subject just about. Shell and BP for example would hire a mathematics graduate from Oxbridge over a engineering graduate from somewhere else for an engineering role. This is because the big operators will train you in your role completely. A real life example was a grad reservoir engineer who has a maths degree from Oxford who was working at Shell and there are many more.
My advice would be do the degree you want to do, get good grades, apply for an oil and gas job. The best jobs for engineers in the oil and gas industry are cushy office jobs like reservoir engineer and petroleum engineer and they accept all STEM degrees virtually.