Not quite - some birther theories assert (based on very strong suspicion) that he is definitely not an NBC. Believe that or not.
However, if you believe in general that a president should not have to be eligible according to the constitution, then no, you’re not a conservative.
Suspicion must be based on evidence and there is no evidence that Momma Obama jetted off the Kenya to give birth to Baby Barack and then smuggled her new born into the United States just in time to have a birth announcement placed in two newspapers.