Your tax person is rightish, but ultimately confused. The IRA custodian is correct. There is no income limit to open or contribute to an IRA, you simply can't deduct the contributions to the IRA if you're over
certain income limits which makes contributing rather pointless (worse than investing in a regular taxable brokerage account) unless you're going to contribute as the first step to making a
backdoor Roth IRA contribution which is only necessary if you're over the
income limits for making direct Roth contributions.
If you've opened, but not funded the IRA just don't fund it and open and fund a Roth IRA instead. If you have funded the IRA you'll just need to call the IRA custodian any time before your tax filing deadline and ask them to recharacterize the IRA contribution to a Roth IRA contribution. They'll move all of the contribution including any gains/losses to a Roth IRA. This makes it as if you had contributed to the Roth in the first place. Note that this is different from a conversion from IRA to Roth IRA (as you would do in a backdoor Roth contribution) which can be a taxable event (gains are taxed), so make sure you use the words "recharacterize my contribution from IRA to Roth IRA" with you custodian.
When you recharacterize a contribution (either IRA to Roth IRA or Roth IRA to IRA) you need to attach a statement to your taxes explaining what you've done so the IRS doesn't get confused when the various forms your custodian will send don't match up. Given your tax preparer's confusion about the IRA I'd be a little concerned they wouldn't know about this, so just make sure they do it. It's possible you don't need to attach a statement if you complete the recharacterization in the same year as the contribution as I've only done it in the first few month few months of the following year (before the tax filing deadline of the year in which I made the contribution).
