I can use both Authnet modules in conjunction with any of the PayPal modules, without any problems.
What do you mean by "in conflict"? I know you said "cannot accept payment" ... but ... I can't see through your eyes what's actually happening, or not.
"Cannot accept payment" could mean "I'm getting an error message, which I'm not telling you about because I didn't think it was important".
It could mean "there's something in the transaction logs but I didn't look at them or know to look at them and share them".
It could mean "they don't show up at checkout".
It could mean "they show up at checkout but suddenly smoke starts coming out of my monitor and I don't know what to do about it".
It could mean "customers are telling me they can't check out but I've not tested a checkout to even know what exact symptoms they're having".
"Conflict" could mean "there's a red alert saying that the sort orders are all the same and I don't know what to do about that".
Or a myriad of additional possibilities.
The more info you give us, the better help we can give you.