If the mutual funds are held in an IRA or 401k or the like there will be no tax until withdrawn. Selling a fund and buying another one is not a withdrawal.
If, however, they are in a regular taxable account, then yes you will have to pay capital gains. However capital gains rates have never every been lower. Some people even have a zero percent rate! See e.g., https://www.thebalance.com/how-to-use-the-zero-percent-tax-rate-on-capital-gains-2388995
Moving to index funds is a very good idea. (IMHO)
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